Abstract
In the present, third survey of reviews of articles on Abelian groups are included papers reviewed during 1972–1978. Here, as in the previous surveys, the questions concerning finite Abelian groups, topological groups, ordered groups, group algebras, modules, structures of subgroups, as well as the questions connected with logic, are not touched on.
Similar content being viewed by others
Literature cited
L. V. Arkhipova, “Abelian groups over distributive lattices,” in: Researches on Group Theory [in Russian], Krasnoyarsk (1975), pp. 3–14.
L. V. Arkhipova, Structure of Abelian Groups Generated by Distributive Lattices [in Russian], Mosk. Gos. Pedagog. Inst., Moscow (1976).
I. S. Bezverkhnyaya, “On the automorphism of subgroups of a free Abelian group,” in: Applied Mathematics [in Russian], No. 2, Tula (1975), pp. 132–135.
I. Kh. Bekker, “On groups of crossed homomorphisms of the automorphism groups of torsion-free Abelian groups,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 7, 3–11 (1973).
I. Kh. Bekker, “On holomorphs of torsion-free Abelian groups,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 3, 3–11 (1974).
I. Kh. Bekker, “On the definability of reduced torsion-free Abelian groups by their own relative holomorphs,” in: Materials Fourth Scientific Conference Mathematics and Mechanics [in Russian], Vol. I, Tomsk Univ., Tomsk, (1974), pp. 105–106.
I. Kh. Bekker, “Abelian groups with isomorphic holomorphs,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 3, 97–99 (1975).
I. Kh. Bekker, “On the definability of reduced Abelian groups by their own holomorphs,” (Editorial Board of Sib. Math. J., Acad. Sci. USSR), Novosibirsk (1976).
I. Kh. Bekker, “On the definability of reduced Abelian groups by their own holomorphs,” Sib. Mat. Zh.,18, No. 1, 226 (1977).
S. D. Berman and Z. P. Zhilinskaya, “On simultaneous direct decompositions of a finitely-generated Abelian group and its subgroup,” Dokl. Akad. Nauk SSSR,210, No. 5, 1004–1007 (1973).
S. D. Berman and Z. P. Zhilinskaya, “On powers of indecomposable pairs of finitely-generated Abelian groups,” in: Proc. Twenty-Eighth Scientific Conf. Prof.-Teaching Staff of Uzhgorod Univ., Math. Sci. Sect. [in Russian], Uzhgorod. Univ., Uzhgorod (1974), pp. 207–226.
I. V. Bobylev, “Projective dimensions of an Abelian group over its own endomorphism ring,” Usp. Mat. Nauk,28, No. 2, 229–230 (1973).
I. V. Bobylev, “Endoprojective dimension of modules,” Sib. Mat. Zh.,16, No. 4, 663–683 (1975).
M. F. Bokshtein, “On the functor of tensor multiplication by an Abelian group in Abelian categories,” Tr. Tbilis. Mat. Inst.,41, 84–99 (1973).
Yu. P. Vasil'ev, “On an abstract characteristic of torsion-free Abelian groups,” in: Algebra [in Russian], No. I, Irkutsk (1972), pp. 3–4.
M. M. Glukhov and S. V. Larin, “Abelian and metabelian groups with regular automorphisms and semiautomorphisms,” Mat. Zametki,12, No. 6, 727–738 (1972).
S. Ya. Grinshpon, “Primary Abelian groups with isomorphic endomorphism groups,” Mat. Zametki,14, No. 5, 733–740 (1973).
S. Ya. Grinshpon, “Fully invariant subgroups of completely decomposable torsion-free Abelian groups,” in: Materials Fourth Scientific Conference Mathematics and Mechanics [in Russian], Vol. I, Tomsk. Univ., Tomsk (1974), pp. 110–111.
S. Ya. Grinshpon, “Almost holomorphically isomorphic Abelian groups,” Tr. Tomsk. Univ.,220, 78–84 (1975).
S. Ya. Grinshpon, “On certain classes of Abelian groups almost isomorphic with respect to fully invariant subgroups,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 2, 23–30 (1976).
A. T. Dzhunisov, “On certain classes of groups with finitely-separable Subgroups,” in: Materials Annual Scientific Summary Conf. Prof.-Teaching Staff, Dedicated to Twenty-Fourth Congress CPSU [in Russian], Kazakhsk. Univ., Alma-Ata (1971), pp. 170–172.
Yu. B. Dobrusin, “Quasi-pure Injective and Transitive Torsion-Free Abelian Groups [in Russian]”, Tomsk. Univ., Tomsk, (1977).
Yu. B. Dobrusin, Quasi-pure Injective Torsion-Free Abelian Groups [in Russian], Tomsk. Univ., Tomsk (1977).
Z. P. Zhilinskaya, “On the isomorphism of pairs of finitely-generated modules,” in: Matterials First Conference Young Scientists, Mem. Sci. Center Acad. Sci, Ukr.SSR, Sect. Math. and Mech. [in Russian], Uzhgorod. Univ., Uzhgorod (1973), pp. 3–12.
Z. P. Zhilinskaya, “On direct decompositions of pairs of finitely-grnerated Abelian groups,” Ukr. Mat. Zh.,26, No. 2, 248–250 (1974).
Z. P. Zhilinskaya, “Description of indecomposable pairs of finitely-generated Abelian groups,” in: Materials Twenty-Ninth Scientific Conf. Prof.-Teaching Staff of Uzhgorod Univ., Math. Sci. Sect. [in Russian], Uzhgorod. Univ., Uzhgorod (1975), pp. 177–194.
A. V. Ivanov, “On a problem of Abelian groups,” Mat. Sb.,105, No. 4, pp. 525–542 (1978).
A. V. Ivanov, “On ω-divisible and ω-flat groups,” Usp. Mat. Nauk,33, No. 1, 213–214 (1978).
A. V. Ivanov, “Classes of torsion Abelian groups closed relative to the taking of epimorphic images and direct limits,” Sib. Mat. Zh.,18, No. 6, 1321–1332 (1977).
A. M. Ivanov, “On the radical theory of Abelian groups,” Mat. Issled.,10, No. 1 (35), 135–143, 298 (1975).
F. F. Kamalov, “Q-groups and Fuchs 5 groups,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 10, 29–36 (1974).
F. F. Kamalov, “On Fuchs 5 groups of cardinality ℵ1.” Izv. Vyssh. Uchebn. Zaved., Mat., No. 8, 46–54 (1975).
F. F. Kamalov, “Intersection of direct summands of Abelian groups,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 5, 45–56 (1977).
R. R. Kel'berer, “On the automorphism group of the direct sum of quasi-cyclic groups,” Uch. Zap. Ivanov. Gos. Pedagog. Inst.,117, 88–94 (1972).
S. F. Kozhukhov, “Pure subgroups of completely decomposable torsion-free Abelian groups of finite rank,” in: Materials Fourth Scientific Conf. Math. and Mech. [in Russian], Vol. I, Tomsk. Univ., Tomsk (1974), p. 112.
S. F. Kozhukhov, Automorphism Groups of Regularly Complete Torsion-free Abelian Groups [in Russian], Tomsk. Univ., Tomsk (1977).
S. F. Kozhukhov, Torsion-free Abelian Groups of Finite Rank with Cyclic Automorphism Groups [in Russian], Tomsk. Univ., Tomsk (1977).
F. V. Krivonos, “On N-high subgroups of Abelian groups,” Vestn. Mosk. Univ., Mat., Mekh., No. 1, 58–64 (1975).
P. A. Krylov, “Extension of isomorphisms in Abelian p-groups,” Mat. Zametki,14, No. 4, 543–548 (1973).
P. A. Krylov, “Radicals of endomorphism rings of torsion-free Abelian groups of finite rank,” in: Materials Fourth Scientific Conference Mathematics and Mechanics [in Russian], Vol. I, Tomsk. Univ., Tomsk (1974), pp. 116–117.
P. A. Krylov, “Radicals of endomorphism rings of torsion-free Abelian groups,” Mat. Sb.,95, No. 2, 214–228 (1974).
P. A. Krylov, “Sums of automorphisms of Abelian groups and the Jacobson radical of an endomorphism ring,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 4, 56–66 (1976).
P. A. Krylov, “Torsion-free Abelian groups with cyclic p-basic subgroups,” Mat. Zametki,20, No. 6, 805–813 (1976).
P. A. Krylov and A. M. Sebel'din, “On the definability of a torsion-free Abelian group by its own endomorphism ring,” in: Materials Fourth Scientific Conference Mathematics and Mechanics [in Russian], Vol. I, Tomsk. Univ., Tomsk (1974), p. 117.
V. I. Kuz'minov, “On groups of pure extensions of Abelian groups,” Sib. Mat. Zh.,17, No. 6, 1308–1320 (1976).
L. Ya. Kulikov, “Conditions under which the group of Abelian extensions is a null group,” Uch. Zap. Mosk. Gos. Pedagog. Inst. im. V. I. Lenina,375, 41–55 (1971).
L. Ya. Kulikov, “Groups of Abelian extensions of a torsion-free group by a torsion group,” in: Fifth Symp. Group Theory. Reports Abstr., Krasnodar [in Russian], Oct. 1–3, 1976, Inst. Mat. Sib. Otd. Akad. Nauk SSSR, Kuban. Univ., Novosibirsk (1976), 116 pp.
A. I. Kuptsov, “Certain properties of the endomorphism group of a commutative regular semigroup,” in: Algebraic Systems with One Algebraic Action. The XXXI Hercen Lectures [in Russian], Leningrad. Gos. Pedagog. Inst. im. A. I. Gertsena, Leningrad (1978), pp. 15–21.
M. I. Kushnir, “Factor-divisible groups of finite rank,” Vestn. Mosk. Univ., Mat. Mekh., No. 2, 48–55 (1972).
M. I. Kushnir, “On completely decomposable groups,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 8, 38–46 (1974).
S. V. Larin, “Abelian groups admitting of automorphisms of order qn free of fixed points,” Mat. Zametki,21, No. 2, 239–249 (1977).
V. M. Lebedenko, “On certain connections between the types of generator systems of Abelian groups and their direct summands,” Preprint No. P5-7344, Soobshch. Ob"edin. Inst. Yader. Issled., Lab. Teor. Fiz., Dubna (1973).
V. M. Lebedenko, “On the generator systems of torsion Abelian groups,” Preprint No. P5-7817, Soobshch. Ob"edin. Inst. Yader. Issled., Lab. Teor. Fiz., Dubna (1974).
V. M. Lebedenko, “On the generator systems of nontorsion Abelian groups of infinite free rank,” Preprint No. P5-10682, Soobshch. Ob"edin. Inst. Yader. Issled., Lab. Teor. Fiz., Dubna (1977).
A. L. Libikh, “Inverse semigroups of local automorphisms of Abelian groups,” in: Studies in Algebra [in Russian], No. 3, Izd. Saratov Univ., Saratov (1973), pp. 25–33.
A. L. Libikh, “On the definability of an Abelian group by its inverse semigroup of local automorphisms,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 6, 62–65 (1976).
A. A. Manovtsev, “Neat hulls in Abelian groups,” Mat. Issled.,8, No. 2 (28), 93–101, 190 (1973).
A. A. Manovtsev, “Inductive purities in Abelian groups,” Mat. Sb.,96, No. 3, 414–446 (1975).
A. A. Manovtsev, “On additive purities in Abelian groups,” Proc. XXV Sci.-Tech. Conf., Math. Sect. [in Russian], Mosk. Inst. Radiotekhn., Elektron. Avtomat., Moscow (1976), pp. 107–111.
L. M. Martynov, “On accessible classes of groups and semigroups,” Mat. Sb.,90, No. 2, 235–245 (1973).
A. P. Mishina, “On automorphisms and endomorphisms of Abelian groups. II,” Vestn. Mosk. Univ., Mat., Mekh., No. 1, 62–66 (1972).
A. P. Mishina, “Abelian groups,” in Progress in Mathematics, Vol. 5: Algebra, Plenum Press, New York (1969), pp. 1–37.
A. P. Mishina, “Abelian groups,” J. Sov. Math.,2, No. 3, 239–263 (1974).
L. S. Mozharovskaya, “On Abelian DLC-groups,” in: Groups with Prescribed Properties of Subgroups [in Russian], Kiev (1973), pp. 216–236.
A. I. Moskalenko, “On factor groups by the center,” Mat. Zametki,10, No. 4, 427–436 (1971).
V. S. Pyatkov, “On the lattice of fully invariant subgroups of one class of separable Abelian groups,” in: Materials Fourth Scientific Conference Mathematics and Mechanics [in Russian], Vol. I, Tomsk. Univ., Tomsk (1974), pp. 119–120.
S. V. Rychkov, “On K-direct sums of Abelian groups,” Mosk. Gos. Pedagog. Inst. im. V. I. Lenina, Moscow (1978).
I. V. Samsonova, “Purities with absolute closure,” Vestn. Mosk. Univ., Mat., Mekh., No. 2, 48–51 (1975).
A. M. Sebel'din, “Conditions for the isomorphism of completely decomposable torsion-free Abelian groups with isomorphic endomorphism rings,” Mat. Zametki,11, No. 4, 403–408 (1972).
A. M. Sebel'din, “Homomorphism groups of completely decomposable torsion-free Abelian groups,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 7, 77–84 (1973).
A. M. Sebel'din, “Complete direct sums of torsion-free Abelian groups of rank 1 with isomorphic endomorphism groups and rings. I,” Mat. Zametki,14, No. 6, 867–878 (1973)
A. M. Sebel'din, “Homomorphism groups of complete direct sums of torsion-free Abelian groups of rank 1,” in: Materials Fourth Scientific Conference Mathematics and Mechanics [in Russian], Vol. I, Tomsk. Univ., Tomsk (1974), pp. 121–122.
A. M. Sebel'din, “Sums of automorphisms of completely decomposable torsion-free Abelian groups,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 2, 85–92 (1975).
A. Yu. Soifer, “A theorem on direct decompositions of Abelian groups,” Mat. Zametki,14, No. 6, 879–884 (1973).
A. Yu. Soifer, “Existence criteria for irreducible generator systems in Abelian groups,” Sib. Mat. Zh.,15, No. 1, 120–151 (1974).
A. Yu. Soifer, “On irreducible generator systems of Abelian groups,” Dokl. Akad. Nauk SSSR,216, No. 2, 274–277 (1974).
At. Stojanova-Venkova, “Basic subgroups of primary Abelian groups,” Plovdiv Univ. Nauchn. Trud.,11, No. 3, 29–32 (1973).
A. I. Tokarenko, “On locally finitely stable automorphism gro-ps,” Latv. Mat. Ezhegodnik,9, 221–223 (1971).
Yu. M. Firsov, “On endomorphisms of subgroups of a free Abelian group,” Uch. Zap. Mosk. Gos. Pedagog. Inst. im. V. I. Lenina,375, 90–99 (1971).
A. A. Fomin, “Tensor product of torsion-free Abelian groups,” Sib. Mat. Zh.,16, No. 5, 1071–1080 (1975).
A. A. Fomin, “Tensor products of torsion-free groups of p-ank 1,” Mosk. Gos. Pedagog. im. V. I. Lenina, Moscow (1975).
A. A. Fomin, “Tensor product of countable torsion-free Abelian groups,” Mat. Issled.,11, No. 38, 197–203 (1976).
L. Fuchs, Infinite Abelian Groups, Vol. I, Academic Press, New York (1970).
L. Fuchs, Infinite Abelian Groups, Vol. II, Academic Press, New York (1973).
M. V. Tsybanev, “On completely M(m)-factorizable Abelian groups,” Ukr. Mat. Zh.,23, No. 5, 699–706 (1971).
A. V. Yakovlev, “The problem of classification of finite-ank Abelian groups without torsion,” J. Sov. Math.,11, No. 4, 660–664 (1979).
E. C. Ackermann, “The construction of diagrams for Abelian groups,” Bull. Austral. Math. Soc.,13, No. 3, 369–373 (1975).
D. L. Armacost, “On pure subgroups of LCA groups,” Proc. Am. Math. Soc.,45, No. 3, 414–418 (1974).
R. Arnal, “n-elèvements de groups abéliens,” C. R. Acad. Sci. Paris,281, No. 18, A759-A761 (1975).
D. M. Arnold, “A duality for quotient divisible Abelian groups of finite rank,” Pacif. J. Math.,42, No. 1, 11–15 (1972).
D. M. Arnold, “A class of pure subgroups of completely decomposable Abelian groups,” Proc. Am. Math. Soc.,41, No. 1, 37–44 (1973).
D. M. Arnold, “Grothendieck and Whitehead groups of torsion free Abelian groups,” Bull. Am. Math. Soc.,79, No. 4, 723–724 (1973).
D. M. Arnold, “On the algebraic K-theory of torsion free Abelian groups of finite rank,” Symposia Mathematica, Vol. XIII, Academic Press, New York-London (1974), pp. 179–193.
D. M. Arnold, “Strongly homogeneous torsion free Abelian groups of finite rank,” Proc. Am. Math. Soc.,56, No. 1, 67–72 (1976).
D. M. Arnold, “Genera and direct sum decompositions of torsion free modules,” in: D. Arnold, R. Hunter, and E. Walker (eds.), Abelian Group Theory, Lect. Notes Math., Vol. 616, Springer-Verlag, Berlin-Heidelberg-New York (1977), pp. 197–218.
D. M. Arnold and E. L. Lady, “Endomorphism rings and direct sums of torsion free Abelian groups,” Trans. Am. Math. Soc.,211, 225–237 (1975).
D. M. Arnold and C. E. Murley, “Abelian groups A, such that Hom(A,-) preserves direct sums of copies of A,” Pacif. J. Math.,56, No. 1, 7–20 (1975).
C. M. Bang, “Partially well-ordered sets of infinite matrices and closed classes of Ahelian groups,” Bull. Austral. Math. Soc.,10, No. 2, 161–167 (1974).
R. A. Beaumont, “Generalizations of quasi-isomorphism,” Symposia Mathematica, Vol. XIII, Academic Press, New York-London (1974), pp. 299–310.
R. A. Beaumont and D. A. Lawver, “Strongly semisimple Abelian groups,” Pacif. J. Math.,53, No. 2, 327–336 (1974).
J. Bečvář, “K-essential subgroups of Abelian groups. I,” Comment. Math. Univ. Carol.,17, No. 3, 481–492 (1976).
J. Bečvář, “K-essential subgroups of Abelian groups. II,” Comment. Math. Univ. Carol.,17, No. 4, 693–707 (1976).
J. Bečvář, “K-essential subgroups of Abelian groups. III,” Comment. Math. Univ. Carol.,18, No. 1, 11–18 (1977).
J. Bečvář and P. Jambor, “On general concept of basic subgroups. II,” Comment. Math. Univ. Carol.,14, No. 3, 471–491 (1973).
K. Benabdallah and R. Bradley, “Sur les groupes quasi-purs-projectifs torsions,” Can. J. Math.,29, No. 1, 107–110 (1977).
K. Benabdallah and R. Bradley, “Sur les groups quasi-purs-projectifs sans torsion,” Comment. Math. Univ. Carol.,18, No. 1, 93–100 (1977).
K. Benabdallah, R. Bradley, and A. Laroche, “Sur les groupes quasi-p-nets injectifs et projectifs,” in: D. Arnold, R. Hunter, and E. Walker (eds.), Abelian Group Theory, Lect. Notes Math., Vol. 616, Springer-Verlag, Berlin-Heidelberg-New York (1977), pp. 228–239.
K. Benabdallah and J. Irwin, “N-high subgroups and p-adic topology,” Comment. Math. Univ. St. Pauli,21, No. 2, 43–45 (1973).
K. Benabdallah and J. Irwin, “Pure N-high subgroups, p-adic topology and direct sums of cyclic groups,” Can. J. Math.,26, No. 2, 322–327 (1974).
K. Benabdallah and J. Irwin, “An application of B-high subgroups of Abelian p-groups,” J. Algebra,34, No. 2, 213–216 (1975).
K. Benabdallah and J. Irwin, “On minimal pure subgroups,” Publ. Math. Debrecen,23, No. 1–2, Separatum, 111–114 (1976).
K. Benabdallah, J. Irwin, and J. Lazaruk, “On pω+n-projective Abelian p-groups,” Comment. Math. Univ. St. Pauli,25, No. 2, 101–105 (1977).
K. Benabdallah, J. Irwin, and M. Rafiq, “N-high subgroups of Abelian p-groups,” Arch. Math.,25, No. 1, 29–34 (1974).
K. Benabdallah, J. Irwin, and M. Rafiq, “A core class of Abelian p-groups,” Symposia Mathematica, Vol. XIII, Academic Press, New York-London (1974), pp. 195–206.
K. Benabdallah and A. Larocche “Quasi-p-pure-injective groups,” Can. J. Math.,29, No. 3, 578–586 (1977)
K. Benabdallah and A. Laroche, “Les groupes abéliens quasi-purs injactifs sans torsion complètement décomposables,” Rend. Math.,10, No. 2–3, 305–312 (1978)).
K. Benabdallah and R. Wilson, “Thick groups and essentially finitely indecomposable groups,” Can. J. Math.,30, No. 3, 650–654 (1978).
G. M. Bergman, “Boolean rings of projection maps,” J. London Math. Soc.,4, No. 4, 593–598 (1972).
W. P. Berlinghoff and J. D. Reid, “Quasi-pure protective and injective torsion groups,” Proc. Am. Math. Soc.,65, No. 2, 189–193 (1977).
F. R. Beyl, “Abelian groups with a vanishing homology group,” J. Pure Appl. Algebra,7, No. 2, 175–193 (1976).
F. R. Beyl and A. Hanna, “Ext.(·,Z)-eproduced Abelian groups are finite,” Acta Math. Acad. Sci. Hung.,28, No. 3–4, 267–269 (1976).
L. Bican, “A note on mixed Abelian groups,” Czech. Math. J.,21, No. 3, 413–417 (1971).
L. Bican, “Completely decomposable Abelian groups any pure subgroup of which is completely decomposable,” Czech. Math. J.,24, No. 2, 176–191 (1974).
L. Bican, “Completely decomposable Abelian groups any regular subgroup of which is completely decomposable,” Czech. Math. J., 25, No. 1, 71–75 (1975).
L. Bican, “Splitting of pure subgroups,” Comment. Math. Univ. Carol.,17, No. 2, 241–249 (1976).
L. Bican, “Factor-splitting Abelian groups of finite rank,” Comment. Math. Univ. Carol.,17, No. 3, 473–480 (1976).
L. Bican “The splitting length of mixed Abelian groups of rank one,” Czech. Math. J.,27, No. 1, 144–154 (1977).
W. Borho, “Über die abelschen Gruppen, auf denen sich nur endlich viele wesentlich verschiedene Ringe definieren lassen,” Abh. Math. Semin, Univ. Hamburg,37, No. 1–2, 98–107 (1972).
F. Castagna, “Endomorphisms of countable direct sums of torsion complete groups,” Acta Math. Acad. Sci. Hung.,23, No. 1–2, 45–50 (1972).
D. Cook, “Totally pure sequences and totally pure projection,” J. Austral. Math. Soc.,21, Part 1, 5–11 (1976).
D. Cook, “Complete exact sequences,” Fund. Math.,92, No. 1, 9–11 (1976).
E. F. Cornelius, Jr., “A generalization of separable groups,” Pacif. J. Math.,39, No. 3, 603–613 (1971).
A. L. S. Corner, “On endomorphism rings of primary Abelian groups. II,” Q. J. Math.,27, No. 105, 5–13 (1976).
A. L. S. Corner, “The independence of Kaplansky's notion of transitivity and full transitivity,” Q. J. Math.,27, No. 105, 15–20 (1976).
E. Coroninas, “Sur une application de l'algèbre ordinale à la théorie des groups abéliens de torsion,” C. R. Acad. Sci. Paris,272, No. 21, A1357-A1359 (1971).
P. Crawley and A. W. Haies, “The structure of Abelian p-groups given by certain presentations. II,” J. Algebra,18, No. 2, 264–268 (1971).
D. O. Cutler, “Completions of topological Abelian p-groups,” Acta Math. Acad. Sci. Hung.,22, No. 3–4, 331–335 (1972).
D. O. Cutler and P. F. Dubois, “Generalized final rank for arbitrary limit ordinals,” Pacif. J. Math.,37, No. 2, 345–351 (1971).
G. Davis, “Orthogonality relations on Abelian groups,” J. Austral. Math. Soc.,19, No. 2, 173–179 (1975).
J. G. Dhombres, “Sur quelques extensions d'homomorphismes,” C. R. Acad. Sci. Paris,281, No. 13, A503-A506 (1975).
G. T. Diderrich, “Sums of lengthl in Abelian groups,” Isr. J. Math.,14, No. 1, 14–22 (1973).
L. Dokas, “Une nouvelle approche à la théorie des groups abéliens p-primaires,” C. R. Acad. Sci. Paris,280, No. 6, A313-A315 (1975).
L. Dokas, “Une nouvelle approche à la théorie des groupes abéliens p-primaires: théorème d'isomorphie,” C. R. Acad. Sci. Paris,280, No. 7, A407-A410 (1975).
L. Dokas, “Une nouvelle approche à la théorie des groupes abéliens p-primaires: esquisse de la démonstration du lemme 3,” C. R. Acad. Sci. Paris,280, No. 13, A869-A871 (1975).
L. Dokas, “Une nouvelle approche à la théorie des groups abéliens p-primaires: esquisse de la démonstration des lemmes auxiliares,” C. R. Acad. Sci. Paris,280, No. 14, A929-A932 (1975).
L. Dokas, “Une nouvelle approche à la théorie des groups abéliens p-primaires: esquisse des démonstrations des théorèmes de prolongement des isomorphismes et d'isomorphie,” C. R. Acad. Sci. Paris,280, No. 17, A1097-A1099 (1975).
A. J. Douglas and H. K. Farahat, “The homological dimension of an Abelian group as a module over its ring of endomorphisms. II,” Monatsh. Math.,76, No. 2, 109–111 (1972).
A. J. Douglas and H. K. Farahat, “The homological dimension of an Abelian group as a module over its ring of endomorphisms. III,” Monatsh. Math.,80, No. 1, 37–44 (1975).
P. F. Dubois, “Generally pα-torsion complete Abelian groups,” Trans. Am. Math. Soc.,159, 245–255 (1971).
J. Duplák, “Rot-quasigroups as isotopes of Abelian groups,” Math. Slovaca,26, No. 4, 287–298 (1976).
P. C. Eklof, “The structure of ultraproducts of Abelian groups,” Pacif. J. Math.,47, No. 1, 67–79 (1973).
P. C. Eklof, “On the existence of k-free Abelian groups,” Proc. Am. Math. Soc.,47, No. 1, 65–72 (1975).
P. C. Eklof, “Homological algebra and set theory,” Trans. Am. Math. Soc.,227, 207–225 (1977).
G. d'Este, “Sui gruppi abeliani il cui anello degli endomorfismi è numerabile e non discreto nella topologia finita,” Atti Ist. Veneto Sci. Lett. Arti, Cl. Sci. Mat. Natur.,134, 239–243 (1975–1976).
K. Faltings, “On the automorphism group of a reduced primary Abelian group,” Trans. Am. Math. Soc.,165, 1–25 (1972).
H. K. Farahat, “Homological dimension and Abelian groups,” in: D. Arnold, R. Hunter, and E. Walker (eds.), Abelian Group Theory, Lect. Notes Math., Vol. 616, Springer-Verlag, Berlin-Heidelberg-New York (1977), pp. 379–383.
F. Fazekas, “Generation of Abelian matrix groups for use in the scattering algebra,” Period. Polytech. Elec. Eng.,16, No. 1, 3–15 (1972).
S. Feigelstock, “On the nilstufe of the direct sum of two groups,” Acta Math. Acad. Sci. Hung.,22, No. 3–4, 449–452 (1972).
S. Feigelstock, “The nilstufe of the direct sum of rank 1 torsion free groups,” Acta Math. Acad. Sci. Hung.,24, No. 3–4, 269–272 (1973).
S. Feigelstock, “On the nilstufe of homogeneous groups,” Acta Sci. Math. (Szeged),36, No. 1–2, 27–28 (1974).
S. Feigelstock, “The nilstufe of rank two torsion free groups,” Acta Sci. Math. (Szeged),36, No. 1–2, 29–32 (1974).
S. Feigelstock, “Extensions of partial multiplications and polynomial identities on Abelian groups,” Acta Sci. Math (Szeged),38, No. 1–2, 17–20 (1976).
S. Feigelstock, “Abelian groups satisfying ring properties,” Comment. Math. Univ. St. Pauli,25, No. 1, 81–87 (1976).
S. Feigelstock, “The absolute annihilator of an Abelian group modulo a subgroup,” Publ. Math. Debrecen,23, No. 3–4, Separatum, 221–224 (1976).
S. Feigelstock, “On the type set of groups and nilpotence,” Comment. Math. Univ. St. Pauli,25, No. 2, 159–165 (1977).
O. Fraser and B. Gordon, “Solution to a problem of L. Fuchs,” Q. J. Math.,25, No. 97, 1–8 (1974).
H. Freedman, “On the additive group of a torsion-free ring of rank two,” Publ. Math. Debrecen,20, No. 1–2, 85–87 (1973).
E. M. Friedlander, “Extension functions for rank 2 torsion free Abelian groups,” Pacif, J. Math.,58, No. 2, 371–380 (1975).
L. Fuchs, Abelian Groups, Pergamon Press Ltd., Oxford (1960).
L. Fuchs, “Note on direct decompositions of torsion-free Abelian groups,” Comment. Math. Helv.,46, No. 4, 409–413 (1971).
L. Fuchs, “Note on extensions of Abelian groups by primary groups,” Arch. Math.,24, No. 1, 1–5 (1973).
L. Fuchs, “On torsion Abelian groups quasi-projective over their endomorphism rings,” Proc. Am. Math. Soc.,42, No. 1, 13–15 (1974).
L. Fuchs, “On solutions of problems listed in my book “Infinite Abelian Groups, Vol. I,” Symposia Mathematica, Vol. XIII, Academic Press, New York-London (1974), pp. 543–548.
L. Fuchs, “Indecomposable Abelian groups of measurable cardinalities,” Symposia Mathematica, Vol. XIII Academic Press, New York-London (1974), pp. 233–244.
L. Fuchs, “On pω+n-protective abelian p-groups,” Publ. Math. Debrecen,23, No. 3–4, Sep aratum, 309–313 (1976).
L. Fuchs, “Valued vector spaces and Abelian p-groups,” Groupe Étude Algèbre, Univ. Pierre et Marie Curie,2, No. 7, 1–12 (1976–1977(1978)).
L. Fuchs and P. Gräbe, “Number of indecomposable summands in direct decompositions of torsion-free Abelian groups,” Rend. Semin. Mat. Univ. Padova,53, 135–148 (1975).
L. Fuchs and J. M. Irwin, “On pω+n-projective p-groups,” Proc. London Math. Soc.30, No. 4, 459–470 (1975).
L. Fuchs and F. Loonstra, “On direct decompositions of torsion-free Abelian groups of finite rank,” Rend. Semin. Mat. Univ. Padova,44, 175–183 (1970).
L. Fuchs and L. Salce, “Abelian p-groups of not limit length,” Comment. Math. Univ. St. Pauli,26, No. 1, 25–33 (1977).
L. Fuchs and G. Viljoen, “Quasi-direct decompositions of torsion-free Abelian groups of infinite rank,” Math. Scand.,33, No. 2, 205–212 (1973).
B. J. Gardner, “Two notes on radicals of Abelian groups,” Comment. Math. Univ. Carol.,13, No. 3, 419–430 (1972).
B. J. Gardner, “Some closure properties for torsion classes of Abelian groups,” Pacif. J. Math.,42, No. 1, 45–61 (1972).
B. J. Gardner, “Generalized-pure-hereditary radical classes of Abelian groups,” Comment. Math. Univ. Carol.,14, No. 2, 187–195 (1973).
B. J. Gardner, “Radicals of Abelian groups and associative rings,” Acta Math. Acad. Sci. Hung.,24, No. 3–4, 259–268 (1973).
B. J. Gardner, “Rings on completely decomposable torsion-free Abelian groups,” Comment. Math. Univ. Carol.,15, No. 3, 381–392 (1974).
B. J. Gardner, “Sub-prime radical classes determined by zero-ings,” Bull. Austral. Math. Soc.,12, No. 1, 95–97 (1975).
B. J. Gardner and D. R. Jackett, “Rings on certain classes of torsion-free Abelian groups,” Comment. Math. Univ. Carol.,17, No. 3, 493–506 (1976).
W. Gaschütz, “Untergruppenkriterien für abelsche Gruppen,” Math. Z.,146, No. 2, 189–199 (1976).
W. Gaschütz, “Subgroup criteria for an Abelian group,” J. Reine Angew. Math.,295, 214–220 (1977).
R. Göbel, “The characteristic subgroups of the Baer-Specker group,” Math. Z.,140, No. 3, 289–292 (1974).
R. Göbel, “Kartesische Produkte von Gruppen,” Arch. Math.,26, No. 5, 454–462 (1975).
B. Goldsmith, “A topological approach to a problem of Nunke,” Arch. Math.,30, No. 3, 271–274 (1978).
K. Golema-Hartman, “Idempotents reducts of Abelian groups and minimal algebras,” Bull. Acad. Pol. Sci., Ser. Sci. Math. Astron. Phys.,21, No. 9, 809–812 (1973).
K. Golema-Hartman, “Exchange property and t-independence,” Colloq. Math.,36, No. 2, 181–186 (1976).
B. Gourteau, “La notion de parallèlisme dans un groupe abélien,” Rev. Roum. Math. Pures Appl.,21, No. 3, 275–285 (1976).
P. Griffith, “ℵn-free Abelian groups,” Q. J. Math.,23, No. 92, 417–425 (1972).
R. Güting, “Subtractive Abelian groups,” Notre Dame J. Form. Log.,16, No. 3, 425–428 (1975).
A. Hales, “Ultrafilters and Abelian groups,” Bull. Am. Math. Soc.,82, No. 4, 554–556 (1976).
A. Hales, “Analogs of the stacked bases theorem,” in: D. Arnold, R. Hunter, and E. Walker (eds.), Abelian Group Theory, Lect. Notes Math., Vol. 616, Springer-Verlag, Berlin Heidelberg-New York (1977), pp. 399–405.
N. Hart, “Determining groups from endomorphism rings for Abelian groups modulo bounded groups,” Acta Math. Acad. Sci. Hung.,22, No. 1–2, 159–162 (1971).
B. Hartley, “Groups of automorphisms of Abelian σ1-groups,” Math. Proc. Cambr. Philos. Soc.,77, No. 2, 241–245 (1975).
G. J. Hauptfleisch, “Torsion-free Abelian groups with isomorphic endomorphism rings,” Arch. Math.,24, No. 3, 269–273 (1973).
J. Hausen, “Automorphisms of Abelian torsion groups with finite p-anks,” Arch. Math.,22, No. 2, 128–135 (1971).
J. Hausen, “Abelian torsion groups with artinian primary components and their automorphisms,” Fund. Math.,71, No. 3, 273–283 (1971).
J. Hausen, “Automorphisms of Abelian p-groups and hyporesidual finiteness,” Rend. Semin. Mat. Univ. Padova,45, 145–156 (1971).
J. Hausen, “On the normal structure of automorphism groups of Abelian p-groups,” J. London Math. Soc.,5, No. 3, 409–413 (1972).
J. Hausen, “Near central automorphisms of Abelian torsion groups,” Trans. Am. Math. Soc.,174, 199–215 [1972(1973)].
J. Hausen, “Primary Abelian groups and the normal structure of their automorphism groups,” in: R. W. Gatterdam and K. W. Weston (eds.), Conference on Group Theory, Lect. Notes Math., Vol. 319, Springer-Verlag, Berlin-Heidelbergr-New York (1973), pp. 119–125.
J. Hausen, “The automorphism group of an Abelian p-group and its normal p-subgroups,” Trans. Am. Math. Soc.,182, 159–164 (1973).
J. Hausen, “The automorphism group of an Abelian p-group and its noncentral normal subgroups,” J. Algebra,30, No. 1–3, 459–472 (1974).
J. Hausen, “Structural relations between general linear groups and automorphism groups of Abelian p-groups,” Proc. London Math. Soc.,28. No. 4, 614–630 (1974).
J. Hausen, “The normal structure of the automorphism group of an Abelian p-group,” Symposia Mathematica, Vol. XIII, Academic Press, New York-London (1974), pp. 21–24.
J. Hausen, “Automorphism groups of Abelian p-groups,” Proc. Am. Math. Soc.,48, No. 1 pp. 67–72 (1975).
J. Hausen, “On automorphism p-groups and endomorphism rings of Abelian p-groups,” Trans. Am. Math. Soc.,210, 123–128 (1975).
J. Hausen, “How automorphism groups reveal Ulm invariants,” J. Algebra,44, No. 1, 9–28 (1977).
J. Hausen and J. A. Johnson, “Characterization of the primary Abelian groups, bounded modulo the divisible subgroup, by the radical of their endomorphism rings,” Arch. Math.,29, No. 6, 566–570 (1977).
J. Hausen and J. A. Johnson, “Abelian groups with many automorphisms,” Rend. Semin. Mat. Univ. Padova,55, 1–5 [1976(1977)].
M. Henjý and S. Znám, “Coset decomposition of the Abelian groups,” Acta Fac. Rerum Natur. Univ. Comen. Math., No. 25, 15–19 (1971).
P. Hill, “The covering theorem for upper basic subgroups,” Mich. Math. J.,18, No. 2, 187–192 (1971).
P. Hill, “Classes of Abelian groups closed under taking subgroups and direct limits,” Algebra Univers,1, No. 1, 63–70 (1971).
P. Hill, “A note on extensions of free groups of torsion groups,” Proc. Am. Math. Soc.,27, No. 1, 24–28 (1971).
P. Hill, “Two problems of Fuchs concerning tor and hom,” J. Algebra,19, No. 3, 379–383 (1971).
P. Hill, “Pure-complete subgroups of direct sums of Prüfer groups,” Glascow Math. J.,13, No. 1, 47–48 (1972).
P. Hill, “The number of isotype andℓ-pure subgroups of an Abelian p-group,” Proc. Am. Math. Soc.,32, No. 1, 69–74 (1972).
P. Hill, “Primary groups whose subgroups of smaller cardinality are direct sums of cyclic groups,” Pacif. J. Math.,42, No. 1, 63–67 (1972).
P. Hill, “The additive group of commutative rings generated by idempotents,” Proc. Am. Math. Soc.,38, No. 3, 499–502 (1973).
P. Hill, “On the splitting of modules and Abelian groups,” Can. J. Math.,26, No. 1, 68–77 (1974).
P. Hill, “New criteria for freeness in Abelian groups,” Trans. Am. Math. Soc.,182, 201–209 (1973).
P. Hill, “Countable unions of totally protective groups,” Trans. Am. Math. Soc.,190, 385–391 (1974).
P. Hill, “A special criterion for freeness,” Symposia Mathematica, Vol. XIII, Academic Press, New York-London (1974), pp. 311–314.
P. Hill, “New criteria for freeness in Abelian groups, II,” Trans. Am. Math. Soc.,196, 191–201 (1974).
P. Hill, “Criteria for freeness in groups and valuated vector spaces,” in: D. Arnold, R. Hunter, and E. Walker (eds.), Abelian Group Theory, Lect. Notes Math., Vol. 616, Springer-Verlag, Berlin-Heidelberg-New York (1977), pp. 140–157.
P. Hill and C. Megibben, “Extensions of torsion complete groups,” Proc. Am. Math. Soc.,44, No. 2, 259–262 (1974).
P. Hill and H. Subramanian, “The freeness of a group based on a distributive lattice,” Proc. Am. Math. Soc.,51, No. 2, 260–262 (1975).
H. L. Miller and S. Shelah, “Singular cohomology in L,” Isr. J. Math.,26, No. 3–4, 313–319 (1977).
M. Horst, “Nilpotente Endomorphismen von freien abelschen Gruppen,” Publ. Math. Debrecen,18, No. 1–4, 261–272 (1971).
Chin-Shui Hsü, “Functorial subgroups commuting with inverse limits,” Math. Ann.,206, No. 3, 177–186 (1973).
Chin-Shui Hsü, “Problem 26 of L. Fuchs,” Proc. Am. Math. Soc.,42, No. 1, 81–84 (1974).
Chin-Shui Hsü, “A class of Abelian groups closed under direct limits and subgroups forma tion,” Pacif. J. Math.,50, No. 2, 495–503 (1974).
M. Huber, “Sur le problème de Whitehead concernant les groupes abéliens libres,” C. R. Acad. Sci. Paris,284, No. 9, A471-A472 (1977).
M. Huber, “Caractérisation des groupes abéliens libres, et cardinalités,” C. R. Acad. Sci. Paris,285, No. 1, A1-A2 (1977).
M. Huber, “Sur les groupes abéliens de la forme Ext (A, G),” C. R. Acad. Sci. Paris,285, No. 8, A529-A531 (1977).
A. Hulanicki, “Unipotent groups of automorphisms of Abelian groups and free products of p-groups,” Symposia Mathematica, Vol. XIII, Academic Press, New York-London (1974), pp. 163–177.
H. Hule and W. Nöbauer, “Local polynomial functions on Abelian groups,” An. Acad. Brasil. Cienc.,49, No. 4, 491–498 (1977).
R. H. Hunter, “Les projectifs et les injectifs des suites exactes équilibrées des groupes abéliens,” C. R. Acad. Sci. Paris,278, A-1395–A1396 (1974).
R. H. Hunter, “Balanced subgroups of Abelian groups,” Bull. Austral. Math. Soc.,13, No. 2, 317–318 (1975).
R. H. Hunter, “Balanced subgroups of Abelian groups,” Trans. Am. Math. Soc.,215, 81–98 (1976).
R. H. Hunter, F. Richman, and E. Walker, “Finite direct sums of cyclic valuated p-groups,” Pacif. J. Math.,69, No. 1, 97–104 (1977).
R. H. Hunter, F. Richman, and E. Walker, “Simply presented valuated Abelian p-groups,” J. Algebra,49, No. 1, 125–133 (1977).
R. H. Hunter, F. Richman, and E. Walker, “Warfield modules,” in: D. Arnold, R. Hunter, and E. Walker (eds.), Abelian Group Theory, Lect. Notes Math., Vol. 616, Springer-Verlag, Berlin-Heidelberg-New York (1977), pp. 87–123.
R. H. Hunter, F. Richman, and E. Walker, “Existence Theorems for Warfield groups,” Trans, Am. Math. Soc.,235, 345–362 (1978).
J. M. Irwin, S. A. Khabbaz, and G. Rayna, “On a submodule of Ext,” J. Algebra,19, No. 4, 486–495 (1971).
R. Ito, “Note on splitting length of Abelian groups,” Proc. Jpn. Acad.,47, No. 6, 527–528 (1971).
R. Ito, “On type-sets of torsion-free Abelian groups of rank 2,” Proc. Am. Math. Soc.,48, No. 1, 39–42 (1975).
P. Jambor and J. Bečvář, “On general concept of basic subgroups,” Comment. Math. Univ. Carol.,13, No. 4, 745–761 (1972).
S. Janakiraman, “Skew projective Abelian groups,” Proc. K. Ned, Akad. Wet. A. Indag. Math.,76, No. 3, 233–236 (1973).
S. Janakiraman and K. M. Rangaswamy, “Strongly pure subgroups of Abelian groups,” in: R. A. Bryce, J. Cossey, and M. F. Newman (eds.), Group Theory, Lect. Notes Math., Vol. 573, Springer-Verlag, Berlin-Heidelberg-New York (1977), pp. 57–65.
S. A. Khabbaz and E. H. Toubassi, “The module structure of Ext(F, T) over the endomorphism ring of T,” Pacif. J. Math.,54, No. 1, 169–176 (1974).
S. A. Khabbaz and E. H. Toubassi, “Ext(A, T) as a module over End(T),” Proc. Am. Math. Soc.,48, No. 2, 269–275 (1975).
S. A. Khabbaz and E. H. Toubassi, “Extensions of Abelian groups of finite rank,” Proc. Am. Math. Soc.,50, No. 1, 115–120 (1975).
J. Kiltinen, “Infinite Abelian groups are highly topologizable.,” Duke Math. J.,41, No. 1, 151–154 (1974).
I. Korec, “On a generalization of Mycielski's and Znám's conjectures about coset decomposition of Abelian groups,” Fund. Math.,85, No. 1, 41–48 (1974).
T. Koyama, “A proof of Dieudonné's theorem on infinite Abelian p-groups,” Nat. Sci. Rep. Ochanomizu Univ.,26, No. 2, 61–62 (1975).
T. Koyama, “On a characterization of quasi-complete p-groups,” Nat. Sci. Rep. Ochanomizu Univ.,27, No. 2, 131–132 (1976).
T. Koyama, “On p-indicators in Ext(Q/Z, T),” Hiroshima Math. J.,8, No. 1, 211–216 (1978).
M. Krasner, “Remarques a propos des récents résultats de M. Lambros Dokas sur les groupes abéliens p-primaires,” C. R. Acad. Sci. Paris,280, No. 19, A1277-A1280 (1975).
M. Krasner, “Encore au sujet des résultats de L. Dokas sur les groupes p-primaires: analogie avec les espaces projectifs,” C. R. Acad. Sci. Paris,280, No. 22, A1499-A1501 (1976).
E. L. Lady, “Countable torsion products of Abelian p-groups,” Proc. Am. Math. Soc.,37, No. 1, 10–16 (1973).
E. L. Lady, “Summands of finite rank torsion free Abelian groups,” J. Algebra,32, No. 1 51–52 (1974).
E. L. Lady, “Almost completely decomposable torsion free Abelian groups,” Proc. Am. Math. Soc.,45, No. 1, 41–47 (1974).
E. L. Lady, “Nearly isomorphic torsion free Abelian Groups,” J. Algebra,35, No. 1–3, 235–238 (1975).
D. A. Lawyer, “Abelian groups in which endomorphic images are fully invariant,” J. Algebra,29, No. 2, 232–245 (1974).
D. A. Lawver and E. H. Toubassi, “Tensor products and the splitting of Abelian groups,” Can. J. Math.,23, No. 5, 764–770 (1971).
M. Le Borgne, “Groupes λ-séparables,” C. R. Acad. Sci. Paris,281, No. 12, A415-A417 (1975).
L. C. A. van Leeuwen, “Remarks on endomorphism rings of torsion-free Abelian groups,” Acta Sci. Math. (Szeged),32, No. 3–4, 345–350 (1971).
L. C. A. van Leeuwen, “On p-pure subgroups of torsion-free cotorsion groups,” Acta Sci. Math. (Szeged),35, No. 1–2, 95–106 (1973).
L. C. A. van Leeuwen, “Some problems and results in Abelian group theory,” Nieuw. Arch. Wisk.,22, No. 2, 143–155 (1974).
L. C. A. van Leeuwen, “On endomorphisms and quasi-endomorphisms of torsion-free groups,” Beitr. Algebra Geom. Wiss. Beitr. M.-Luther-Univ. Halle-Wittenberg, No. 4, 15–22 (1975).
I. Lehmann, “Axiomatische Charakterisierung abelscher Gruppen mit Hilfe der Umkehroperationen,” Wiss. Z. Humboldt-Univ. Berlin Math. Naturwiss. R.,23, No. 5, 471–478 (1974).
K. M. Lesko, “A generalization to almost divisible groups,” Pi Mu Epsilon J.,6, No. 6, 345–347 (1977).
W. Liebert, “Ulm valuations and co-valuations on torsion-complete p-groups,” in: D. Arnold, R. Hunter, and E. Walker (eds.), Abelian Group Theory, Lect. Notes Math., Vol. 616, Springer-Verlag, Berlin-Heidelberg-New York (1977), pp. 337–353.
R. C. Linton, “Abelian groups in which every neat subgroup is a direct summand,” Publ. Math. Debrecen,20, No. 1–2, 157–160 (1973).
R. C. Linton, “On fully invariant subgroups of primary Abelian groups,” Mich. Math. J.,22, No. 3, 281–284 (1976).
R. C. Linton and C. Megibben, “Extensions of totally projective groups,” Proc. Am. Math. Soc.,64, No. 1, 35–38 (1977).
F. Loonstra, “Remark on the maximal torsion subgroup of Abelian group,” in: Beitr. Algebra Geom., Vol. 3, Berlin (1974), pp. 55–57.
A. Mader, “The fully invariant subgroups of reduced algebraically compact groups,” Publ. Math. Debrecen,17, No. 1–4, 299–306 (1970).
A. Mader, “Splitting of mixed Abelian groups,” J. Reine Angew. Math.,262–263, 261–270 (1973).
A. Mader, “The p-adic hull of Abelian groups,” Trans. Am. Math. Soc.,187, No. 1, 217–229 (1974).
A. Mader, “Finite order extensions of a primary group by a torsion-free group,” Acta Math. Acad. Sci. Hung.,28, No. 3–4, 335–342 (1976).
A. Mader, “A Galois correspondence in Abelian groups,” in: D. Arnold, R. Hunter, and E. Walker (eds.), Abelian Group Theory, Lect. Notes Math., Vol. 616, Springer-Verlag, Berlin-Heidelberg-New York (1977), pp. 384–391.
G. de Marco, “On the algebraic compactness of some quotients of product groups,” Rend. Semin. Mat. Univ. Padova,53, 329–333 (1975).
W. May and E. Toubassi, “Endomorphisms of Abelian groups and the theorem of Baer and Kaplansky,” J. Algebra,43. No. 1, 1–13 (1976).
W. May and E. Toubassi, “A result on problem 87 of L. Fuchs,” in: D. Arnold, R. Hunter, and E. Walker (eds.), Abelian Group Theory, Lect. Notes Math., Vol. 616, Springer-Ver lag, Berlin-Heidelberg-New York (1977), pp. 354–367.
W. May and E. Toubassi, “Embedding of totally protective groups,” Arch. Math.,29, No. 5, 465–471 (1977).
C. Megibben, “On pα-high injectives,” Math. Z.,122, No. 2, 104–110 (1971).
C. Megibben, “Generalized pure injectivity,” Symposia Mathematica, Vol. XIII, Academic Press, New York-London (1974), pp. 257–271.
C. Megibben and E. Toubassi, “Tensor products of mixed Abelian groups,” J. Algebra,38, No. 2, 345–358 (1976).
A. R. Meijer, “A note on separable homogeneous extensions of the Specker group,” Arch. Math.,24, No. 2, 123–125 (1973).
A. R. Meijer and G. Viljoen, “A note on the extension of the infinite cyclic group and realizable groups,” Arch. Math.,25, No. 2, 113–120 (1974).
A. Mekler, “The number of k-free Abelian groups and the size of Ext,” in: D. Arnold, R. Hunter, and E. Walker (eds.), Abelian Group Theory, Lect. Notes Math., Vol. 616, Springer-Verlag, Berlin-Heidelberg-New York (1977), pp. 323–331.
C. Metelli and L. Salce, “The endomorphism ring of an Abelian torsion-free homogeneous separable group,” Arch. Math.,26, No. 5, 480–485 (1975).
R. Mines, “A different completion functor,” in: D. Arnold, R. Hunter, and E. Walker (eds.), Abelian Group Theory, Lect. Notes Math., Vol. 616, Springer-Verlag, Berlin-Heidelberg-New York (1977), pp. 392–398.
G. S. Monk, “Essentially indecomposable Abelian p-groups,” J. London Math. Soc.,3, No. 2, 341–345 (1971).
G. S. Monk, “On the endomorphism ring of an Abelian p-group and of a large subgroup,” Pacif. J. Math.,41, No. 1, 183–193 (1972).
J. D. Moore and H. Bowman, “A note on the large subgroup topology for Abelian groups,” Comment. Math. Univ. St. Pauli,22, No. 2, 7–17 (1974).
J. D. Moore and H. Bowman, “A method for obtaining proper classes of short exact sequences of Abelian groups,” Publ. Math. Debrecen,24, No. 1–2, 59–63 (1977).
J. D. Moore and E. J. Hewett, “On fully invariant subgroups of Abelian p-groups,” Comment. Math. Univ. St. Pauli,20, No. 2, 97–106 (1972).
J. D. Moore and E. J. Hewett, “Abelian groups in which every α-pure subgroup is β-pure,” Can. J. Math.,25, No. 3, 560–566 (1973).
C. E. Murley, “The classification of certain classes of torsion free Abelian groups,” Pacif. J. Math.,40, No. 3, 647–665 (1972).
C. E. Murley, “Direct products and sums of torsion-free Abelian groups.,” Proc. Am. Math. Soc.,38, No. 2, 235–241 (1973).
O. Mutzbauer, “Klassifizierung torsionfreier abelscher Gruppen des Ranges 2,” Rend. Semin. Mat. Univ. Padova,55, 195–208 (1976(1977)).
T. Nordahl, “Abelian groups and N-semigroups. II,” Proc. Jpn. Acad.,53, No. 1, 8–10 (1977).
R. J. Nunke, “Uniquely elongating modules,” Symposia Mathematica, Vol. XIII, Academic Press, New York-London (1974), pp. 315–330.
R. J. Nunke, “Whitehead's problem,” in: D. Arnold, R. Hunter, and E. Walker (eds.), Abelian Group Theory, Lect. Notes Math., Vol. 616, Springer-Verlag, Berlin-Heidelberg-New York (1977), pp. 240–250.
A. Orsatti, “Anelli de endomorfismi di gruppi abeliani senza torsione,” Symposia Mathematica, Vol. VIII, Academic Press, New York-London (1972), pp. 179–191.
A. Orsatti, “Alcuni aspetti della teoria dei gruppi abeliani,” Bull. Unione Mat. Ital.,A13, No. 3, 485–533 (1976).
J. T. Parr, “Endomorphism rings of rank two torsion-free Abelian groups,” Proc. London Math. Soc.,22, No. 4, 611–632 (1971).
E. J. Peake, Jr., “On Serre classes of Abelian groups,” Math. Stud.,43, No. 1–2, 42–48 (1975).
S. Piccard, “Sur les bases des groupes multiplicatifs abéliens libres,” Publ. Cent. Rech. Math. Pures, Sér. A, No. 12, 1–6 (1977).
J. Plonka, “On the arity of idempotent reduct of Abelian groups,” Colloq. Math.,27, No. 2, 175–176 (1973).
G. D. Poole and J. D. Reid, “Abelian groups quasi-injective over their endomorphism rings,” Can. J. Math.,24, No. 4, 617–621 (1972).
T. Porter, “The first derived equalizer of a pair of Abelian group homomorphisms,” Proc. Am. Math. Soc.,42, No. 1, 77–80 (1974).
L. M. Pretorius and M. J. Schoeman, “A note on PT-groups,” Proc. K. Ned. Akad. Wet.,A78: Indag. Math.,37, No. 3, 224–229 (1975).
L. Procházka, “A consequence of a theorem of L. Fuchs,” Comment. Math. Univ. Carol.,13, No. 1, 177–179 (1972).
G. Pufter, “Antinil groups,” Tamkang J. Math.,6, No. 2, 105–108 (1975).
K. M. Rangaswamy, “Abelian groups with self-injective endomorphism rings,” in: M. F. Newman (ed.), The Theory of Groups, Lect. Notes Math., Vol. 372, Springer-Verlag, Berlin-Heidelberg-New York (1974), pp. 595–604.
J. D. Reid, “On rings on groups,” Pacif. J. Math.,53, No. 1, 229–237 (1974).
J. D. Reid, “Quasi-pure-injectivity and quasipure-prajectivity,” in: D. Arnold, R. Hunter, ad E. Walker (eds.), Abelian Group Theory, Lect. Notes Math., Vol. 616, Springer Verlag, Berlin-Heidelberg-New York (1977), pp. 219–227.
F. Richman, “Detachable p-groups and quasi-injectivity,” Acta Math. Acad. Sci. Hung.,27, No. 1–2, 71–73 (1976).
F. Richman, “Computing heights in Tor,” Houston J. Math.,3, No. 2,267–271 (1977).
F. Richman, “A guide to valuated groups,” in: D. Arnold, R. Hunter, and E. Walker (eds.), Abelian Group Theory, Lect. Notes Math., Vol. 616, Springer-Verlag, Berlin-Heidelberg-New York (1977), pp. 73–86.
F. Richman and E. A. Walker, “Homological dimension of Abelian groups over their endomorphism rings,” Proc. Am. Math. Soc.,54, No. 1, 65–68 (1976).
F. Richman and E. A. Walker, “Ext in pre-Abelian categories,” Pacif, J. Math.,71, No. 2, 521–535 (1977).
L. A. Rogers, “Ulm's theorem for partially ordered structures related to simply presented Abelian p-groups,” Trans. Am. Math. Soc.,227, 333–343 (1977).
L. A. Rogers, “The structure of p-trees: algebraic systems related to Abelian groups,” in: D. Arnold, R. Hunter, and E. Walker, (eds.), Abelian Group Theory, Lect. Notes Math., Vol. 616, Springer-Verlag, Berlin-Heidelberg-New York (1977), pp. 57–72.
J. Rotman, “Sheaves and Abelian groups,” Symposia Mathematica, Vol. XIII, Academic Press New York-London (1974), pp. 11–20.
L. Salce, “Sull'anello degli endomorfismi dei gruppi abeliani, ridotti e liberi da torsione,” Atti Ist. Veneto Sci., Lett. Arti, Cl. Sci. Mat. Natur.,128, 401–410 (1969–1970).
L. Salce and F. Menegazzo, “Abelian groups whose endomorphism ring is. linearly compact,” Rend. Semin. Mat. Univ. Padova,53, 315–325 (1975).
Z. Samadeni and T. Swirszcz, “Reflective and coreflective subcategories of categories of Banach spaces and Abelian groups,” Bull. Acad. Pol., Sci., Ser. Sci. Math., Astron. Phys.,25, No. 11, 1105–1107 (1977).
M. J. Schoeman, “On splitting extensions by torsion groups,” Proc. Ned. Akad. Wet.,A76; Indag. Math.,35, No. 2, 132–136 (1973).
M. J. Schoeman, “Injective properties of torsion-complete mixed groups,” An. Şti. Univ. Iaşi, Sec. la,22, No. 1, 11–13 (1976).
P. Schultz, “On a paper of Szele and Szendrei on groups with commutative endomorphism rings,” Acta Math. Acad. Sci. Hung.,24, No. 1–2, 59–63 (1973).
P. Schultz, “The endomorphism ring of the additive group of a ring,” J. Austral. Math. Soc.,15, No. 1, 60–69 (1973).
P. Schultz, “Torsion-free extensions of torsion-free Abelian groups,” J. Algebra,30, No. 1–3, 75–91 (1974).
S. Shelah, “Infinite Abelian groups, Whitehead problem and some constructions,” Isr. J. Math.,18, No. 3, 243–256 (1974).
S. Shelah, “A compactness theorem for singular cardinals, free algebras, Whitehead problern and transversals,” Isr. J. Math.,21, No. 4, 319–349 (1975).
S. Shelah, “Existence of rigidlike families of Abelian p-groups,” in: D. H. Saracino and V. B. Weispfenning (eds.), Model Theory and Algebra, Lect. Notes Math., Vol. 498, Springer-Verlag, Berlin-Heidelberg-New York (1975), pp. 384–402.
B. Sobociński, “Concerning the postulate-system of subtractive Abelian groups,” Notre Dame J. Form. Log.,16, No. 3, 429–444 (1975).
D. Spellman, “The structure of the Abelian groups Fn/(Fn. F),” J. Algebra,40, No. 2, 301–308 (1976).
R. Stanton, “Decomposition bases and Ulm's theorem,” in: D. Arnold, R. Hunter, and E. Walker (eds.), Abelian Group Theory, Lect. Notes Math., Vol. 616, Springer-Verlag, Berlin-Heidelberg-New York (1977), pp. 39–56.
R. Stantan, “Infinite decomposition bases,” Pacif. J. Math.,70, No. 2, 549–566 (1977).
A. E. Stratton, “A splitting theorem for mixed Abelian groups,” Symposia Mathematica, Vol. XIII, Academic Press, New York-London (1974), pp. 109–125.
R. Strecker, “Induktive Isomorphie unendlicher abelscher Gruppen,” Monatsber. Dtsch. Akad. Wiss. Berlin,13, No. 2, 81–86 (1971).
R. W. Stringall, “Decompositions of Abelian p-groups,” Proc. Am. Math. Soc.,28, No. 2, 409–410 (1971).
A. Szendrei, “Idempotent reducts of Abelian groups,” Acta Sci. Math. (Szeged),38, No. 1–2, 171–182 (1976).
D. Tabor, “Homomorphisms of torsion complete Abelian p-groups,” Arch. Math.,24, No. 1, 6–13 (1973).
S. W. Talley, “Niceness of the socle and a characterization of groups of bounded order,” Pi Mu Epsilon J.,5, No. 10, 497–502 (1974).
D. Tarwater, “Orbits of basic subgroups of primary Abelian groups under automorphisms,” Texas J. Sci.,23, No. 3, 431–433 (1972).
N. Tone, “On Abelian groups with a certain property on essential subgroups,” Comment. Math. Univ. St. Pauli,19, No. 2, 127–129 (1971).
E. H. Toubassi, “On the group of extensions,” Acta Math. Acad. Sci. Hung.,24, No. 1–2, 87–92 (1973).
E. H. Toubassi, “The group of extensions and the splitting length,” Can. J. Math.,26, No. 4, 879–883 (1974).
E. H. Toubassi and D. A. Lawver, “Height-slope and splitting length of Abelian groups,” Publ. Math. Debrecen,20, No. 1–2, 63–71 (1973).
C. Vinsonhaler, “Torsion free Abelian groups quasi-projective over their endomorphism rings. II,” Pacif. J. Math.,74, No. 1, 261–265 (1978).
C. Vinsonhaler and W. J. Wickless, “Completely decomposable groups which admit only nilpotent multiplications,” Pacif. J. Math.,53, No. 1, 273–280 (1974).
C. Vinsonhaler and W. J. Wickless, “Torsion free Abelian groups quasi-projective over their endomorphism rings,” Pacif. J. Math.,68, No. 2, 527–535 (1977).
C. L. Walker, “Projective classes of cotorsion groups,” I11. J. Math.,17, No. 4, 689–706 (1973).
C. L. Walker, “Local quasi-isomorphisms of torsion free Abelian groups,” I11. J. Math.,18, No. 4, 537–551 (1974).
C. L. Walker, “Local-quasi-endomorphism rings of rank one mixed Abelian groups,” in: D. Arnold, R. Hunter, and E. Walker (eds.), Abelian Group Theory, Lect. Notes Math., Vol. 616, Springer-Verlag, Berlin-Heidelberg-New York (1977), pp. 368–378.
E. A. Walker, “Ulm's theorem for totally projective groups,” Proc. Am. Math. Soc.,37, No. 2, 387–392 (1973).
E. A. Walker, “The groups pβ. “Symposia Mathematica, Vol. XIII, Academic Press, New York-London (1974), pp. 245–255.
K. D. Wallace, “On mixed groups of torsion-free rank one with totally projective primary components,” J. Algebra,17, No. 4, 482–488 (1971).
K. D. Wallace, “Cλ-groups and λ-basic subgroups,” Pacif. J. Math.,43, No. 3, 709–809 (1972).
R. B. Warfield, Jr., “Classification theorems for p-groups and modules over a discrete valuation ring,” Bull. Am. Math. Soc.,78, No. 1, 88–92 (1972).
R. B. Warfield, Jr., “Extensions of torsion-free Abelian groups of finite rank,” Arch. Math.,23, No. 2, 145–150 (1972).
R. B. Warfield, Jr., “The uniqueness of elongations of Abelian groups,” Pacif. J. Math.,52, No. 1, 289–304 (1974.
R. B. Warfield, Jr., “A classification theorem for Abelian p-groups,” Trans. Am. Math. Soc.,210, 149–168 (1975).
R. B. Warfield, Jr., “Classification theory of Abelian groups. I, Balanced Projectives,” Trans. Am. Math. Soc.,222, 33–63 (1976).
R. B. Warfield, Jr., “The structure theory of mixed Abelian groups,” in: D. Arnold, R. Hunter, and E. Walker (eds.), Abelian Group Theory, Lect. Notes Math., Vol. 616, Springer-Verlag, Berlin-Heidelberg-New York (1977), pp. 1–38.
C. Webb, “Transformations on tensor products and torsionless property in Abelian groups,” Bull. Austral. Math. Soc.,14, No. 3, 389–396 (1976).
M. C. Webb, “A bound for the nilstufe of a group,” Acta Sci. Math. (Szeged),39, No. 1–2, 185–188 (1977).
J. Werth, Jr., “Maximal pure subgroups of torsion complete Abelian p-groups,” Pacif. J. Math.,51, No. 1, 307–316 (1974).
W. J. Wickless, “Abelian groups which admit only nilpotent multiplications,” Pacif. J. Math.,40, No. 1, 251–259 (1972).
W. J. Wickless and C. Vinsonhaler, “A note on torsion-free Abelian groups of finite rank,” Proc. Am. Math. Soc.,39, No. 1, 63–68 (1973).
J. Winthrop, “A homological characterization of large subgroups,” Acta Math. Acad. Sci. Hung.,25, No. 3–4, 255–262 (1974).
S. M. Yahya, “On cogenerators in Abelian groups,” Acta Math. Acad. Sci. Hung.,28, No. 1–2, 25–32 (1976).
F. Yoshida, “On Abelian p-groups satisfying certain conditions on heights,” Comment. Math. Univ. St. Pauli,25, No. 2, 145–148 (1977).
H. Zöschinger, “Über torsions- und x-Elemente von Ext(C, A),” J. Algebra,50, No. 2, 299–336 (1978).
Additional information
Translated from Itogi Nauki i Tekhniki, Algebra, Topologiya, Geometriya, Vol. 17, pp. 3–63, 1979.
Rights and permissions
About this article
Cite this article
Mishina, A.P. Abelian groups. J Math Sci 18, 629–668 (1982). https://doi.org/10.1007/BF01091961
Issue Date:
DOI: https://doi.org/10.1007/BF01091961