Keywords
- Normal Subgroup
- Abelian Subgroup
- Finite Index
- Soluble Group
- Infinite Group
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References
B. Amberg, ‘Abelian factorizations of infinite groups', Math. Z. 123(1971), 201–214.
B. Amberg, ‘Factorizations of infinite groups', Habilitationsschrift, Univerität Mainz, Mai 1973.
B. Amberg, ‘Artinian and noetherian factorized groups', Rend. Sem. Mat. Univ. Padova 55(1976), 105–122.
B. Amberg, ‘Factorizations of infinite soluble groups', Rocky Mountain J. Math 7(1977), 1–17.
B. Amberg, ‘Über auflösbare Produkte nilpotenter Gruppen', Arch. Math. (Basel) 30(1978), 361–363.
B. Amberg, ‘Lokal endlich-auflösbare Produkte von zwei hyperzentralen Gruppen', Arch. Math. (Basel) 35(1980), 228–238.
B. Amberg, ‘Über den Satz von Kegel und Wielandt', Arch. Math. (Basel) 40(1983), 289–296.
B. Amberg, ‘Soluble products of two locally finite groups with min-p for every prime p', Rend. Sem. Mat. Padova 69(1983), 7–17.
B. Amberg, ‘Factorized groups with max, min, and min-p', Can. Math. Bull. 27(1984), 171–178.
B. Amberg, ‘Products of two abelian subgroups” Rocky Mountain J. Math. 14(1984), 541–547.
B. Amberg, ‘On groups which are the product of abelian subgroups', Glasgow Math. J. 26(1985), 151–156.
B. Amberg, ‘Produkte von Gruppen mit endlichem torsionsfreiem Rang', Arch. Math. (Basel) 45(1985), 398–406.
B. Amberg, ‘Products of groups with finite rank', Arch. Math. (Basel) 49(1987), 369–375.
B. Amberg, ‘Infinite factorized groups: results and problems', Workshop on Algebra and Number Theory, Pusan, South Korea, 1987.
B. Amberg, S. Franciosi and F de Giovanni, ‘On normal subgroups of products of nilpotent groups', J. Austral Math. Soc. (Ser. A) 44(1988), 275–286.
B. Amberg, S. Franciosi and F de Giovanni, ‘Groups with a nilpotent triple factorization', Bull. Austral Math. Soc. 37(1988), 69–79.
B. Amberg, S. Franciosi and F de Giovanni, ‘Groups with an FC-nilpotent triple factorization', Ricerche Mat., to appear.
B. Amberg, F. Franciosi and F de Giovanni, ‘Groups with a supersoluble triple factorization', J. Algebra 117(1988), 136–148.
B. Amberg, F. Franciosi and F de Giovanni, ‘On trifactorized soluble minimax groups', Arch. Math. (Basel) 51 (1988), 13–19.
B. Amberg, S. Franciosi and F de Giovanni, 'soluble groups which are the product of a nilpotent and polycyclic subgroup', Proceedings of the Singapore Group Theory Conference, (1987).
B. Amberg, S. Franciosi and F de Giovanni, ‘Nilpotent-by-noetherian factorized groups', Canad. Math. Bull., to appear.
B. Amberg, S. Franciosi and F de Giovanni, ‘Triply factorized groups', to appear.
B. Amberg and N. Halbritter, ‘On groups with a triple factorization', to appear.
B. Amberg and R. Moghaddam, ‘Products of locally finite groups with min-p', J. Austral Math. Soc. (Ser. A) 41(1968), 352–360.
B. Amberg und T. Müller, ‘Rangfunktionen für Produkte von Untergruppen', to appear.
B. Amberg and D.J.S. Robinson, ‘Soluble groups which are products of nilpotent minimax groups', Arch. Math. (Basel) 42(1984), 385–390.
B. Amberg and W.R. Scott, ‘Products of abelian subgroups', Proc. Amer. Math. Soc. 26(1970), 541–547.
M. Blaum, ‘Factorizations of the simple groups PSL (3,q) and PSU(3,q 3)', Arch. Math. 40(1983), 8–13.
W. Brisley and I.D. MacDonald, ‘Two classes of metabelian p-groups', Math. Z. 112(1969), 5–12.
C.J.B. Brookes, ‘Ideals in group rings of soluble groups of finite rank', Math. Proc. Camb. Phil. Soc. 97(1985), 27–49.
N.S. Chernikov, ‘Infinite groups that are products of nilpotent subgroups', Dokl. Akad. Nauk SSSR 252(1980), 57–60.
N.S. Chernikov, ‘Groups which are factorized by extremal subgroups', Ukrain. Mat. Zh. 32(1980), 707–711.
N.S. Chernikov, ‘Some factorization theorems for infinite groups', Dokl. Akad. Nauk SSSR 255(1980), 537–539.
N.S. Chernikov, ‘On factorized locally finite groups', Sibir. Mat. Zh. 21(1980), 186–195.
N.S. Chernikov, ‘Products of almost abelian groups', Ukrain. Mat. Zh 33(1981), 136–138.
N.S. Chernikov, ‘Products of groups of finite rank', Algebra i Logika 20(1981), 315–329.
N.S. Chernikov, ‘On particular factorization of locally finite groups', A study of groups with given characteristic system of subgroups, Akad. Nauk Ukrain. SSSR, Inst. Mat., Kiev (1981), 25–34.
N.S. Chernikov, ‘Factorized locally graduated groups', Dokl. Akad. Nauk SSSR 260(1981), 543–546.
N.S. Chernikov, ‘Locally graduated groups factorized by subgroups of finite rank', Algebra i Logika 21(1982), 108–120.
N.S. Chernikov, ‘Sylow subgroups of factorized periodic linear groups', A subgroup characterization of groups, Akad. Nauk Ukrain. SSSR, Inst. Mat., Kiev (1982), 35–52.
N.S. Chernikov, ‘On factorized locally finite groups satisfying the minimal condition on primary subgroups', A subgroup characterization of groups, Akad. Nauk Ukrain. SSSR, Inst. Mat., Kiev (1982), 52–73.
N.S. Chernikov, ‘Factorization theorem for locally graduated groups', Ukrain. Mat. Zh. 34(1982), 732–737.
N.S. Chernikov, ‘Infinite groups decomposed as a product of pairwise permutable subgroups', Dokl. Akad. Nauk SSSR Ser. A 11(1983), 24–27.
N.S. Chernikov, ‘Products of groups of finite free rank', Groups and systems of their subgroups, Akad. Nauk Ukrain. SSSR, Inst. Mat., Kiev (1983), 42–56.
N.S. Chernikov, ‘Factorizations of infinite groups in pairwise permutable subgroups', Construction of groups and their subgroup characterization, Akad. Nauk Ukrain. SSSR, Inst. Mat., Kiev (1984), 47–66.
N.S. Chernikov, ‘Factorizations of infinite groups under finiteness conditions', Dokl. Akad. Nauk SSSR Ser. A 5(1985), 26–29.
N.S. Chernikov, ‘Properties of the normal closure of the centre of an FC-subgroup B of a group G=AB with abelian subgroup A', Ukrain. Mat. Zh. 36(1986), 364–368.
N.S. Chernikov, ‘Groups which are products of permutable subgroups', Akad. Nauk Ukrain. SSSR, Inst. Mat., Kiev (1987).
P.M. Cohn, ‘A remark on the general product of two infinite cyclic groups', Arch. Math. (Basel) 7(1956), 94–99.
E. Fisman and Z. Arad, ‘A proof of Szep's conjecture on non-simplicity of certain finite groups', J. Alg. 108(1987), 340–354.
N. Halbritter, ‘Groups with a nilpotent-by-finite triple factorization', Arch. Math. (Basel), to appear.
H. Heineken, ‘Produkte abelscher Gruppen und ihre Fittinggruppe', Arch. Math. (Basel), 48(1987),185–192.
H. Heineken and J.C. Lennox, ‘A note on products of abelian groups', Arch. Math. (Basel), 41(1983), 498–501.
D.F. Holt and R.B. Howlett, ‘On groups which are the product of two abelian groups', J. London Math. Soc. 29(1984), 453–461.
R.B. Howlett, ‘On the exponent of certain factorirable groups', J. London Math. Soc. 31(1985), 265–271.
B. Huppert, Endliche Gruppen I, Springer, Berlin (1967).
N. Itô, ‘Über das Produkt von zwei abelschen Gruppen', Math. Z. 62(1955), 400–401
N. Itô, ‘On the factorizations of the linear fractional group LF(2,p)', Acta. Math. Soc. (Szeged) 15(1953), 79–84.
L.S. Kazarin, ‘On a problem of Szep', Mat. USSR Izvestiya 28(1987), 467–495.
O.H. Kegel, ‘Produkte nilpotenter Gruppen', Arch. Math. (Basel) 12(1961), 90–93.
O.H. Kegel, ‘On the solubility of some factorized linear groups', Illinois J. Math. 9(1965), 535–547.
O.H. Kegel, ‘Zur Struktur mehrfach faktorisierter endlicher Gruppen', Math. Z. 87(1965), 42–48.
O.H. Kegel and B.A.F. Wehrfritz, Locally finite groups, North-Holland, Amsterdam (1973).
J.C. Lennox and J.E. Roseblade, ‘Soluble products of polycyclic groups', Math. Z. 170(1980), 153–154.
E. Pennington, ‘On products of finite nilpotent groups', Math. Z. 134(1973), 81–83.
E. Pennington, ‘Trifactorizable groups', Bull. Austral. Math. Soc. 8(1973), 461–469.
L. Rédei, ‘Zur Theorie der faktorisierbaren Gruppen. I.', Acta Math. Hung. 1(1950), 74–98.
D.J.S. Robinson, Finiteness conditions and generalized soluble groups, Part I and II, Springer, Berlin (1972).
D.J.S. Robinson, ‘The vanishing of certain homology and cohomology groups', J. Pure Appl. Algebra 7(1976), 145–167.
D.J.S. Robinson, A course in the theory of groups, Springer, Berlin (1980).
D.J.S. Robinson, ‘Infinite factorized groups', Rend. Sem. Mat. Fis. Milano 53(1983), 347–355.
D.J.S. Robinson, ‘Soluble products of nilpotent groups', J. Algebra 98(1986), 183–196.
D.J.S. Robinson, ‘Cohomology of locally nilpotent groups', J. Pure Appl. Algebra 48(1987), 281–300.
J.E. Roseblade, ‘Group rings of polycyclic groups', J. Pure Appl. Algebra 3(1973), 307–328.
W.R. Scott, Group Theory, Prentice-Hall, England Cliffs, N.J. (1964).
N.F. Sesekin, ‘On the product of two finitely connected abelian groups', Sibir Mat. Z. 9(1968), 1427–1430.
N.F. Sesekin, ‘On the product of two finitely generated abelian groups', Mat. Zametki 13(1973), 266–268.
S.E. Stonehewer, 'subnormal subgroups of factorized groups', Lecture Notes in Math. 1281, Proceedings Brixen/Bressanone (1986), 158–175.
N.M. Suchkov, ‘Example of a mixed group factorized by two periodic subgroups', Algebra i Logika 23(1984), 573–577.
N.M. Suchkov, ‘Subgroups of a product of locally finite groups', Algebra i Logika 24(1985), 408–413.
Y.P. Sysak, ‘Products of infinite groups', Preprint 82.53, Akad. Nauk Ukrain. Inst. Mat., Kiev (1982), 1–36.
Y.P. Sysak, ‘Products of locally cyclic, torsion-free groups', Algebra i Logika 25(1986), 672–686.
H. Thiel, ‘Die Faktorisationen der Gruppen PSL(2,K), PSL(3,K) und PSU(3,K) für einen lokal endlichen Körper', Diplomarbeit, Universität Mainz (1983).
M.J. Tomkinson, ‘Products of abelian subgroups', Arch. Math. (Basel) 47(1986), 107–122.
H. Völklein, ‘Algebraic groups as products of two subgroups, one of which is solvable', Houston J. Math. 12(1986), 145–154.
H. Wielandt, ‘Über das Produkt von paarweise vertauschbaren nilpotenten Gruppen', Math. Z. 65(1951), 1–7.
H. Wielandt, ‘Über Produkte nilpotenter Gruppen', Illinois J. Math. 2(1958), 611–618.
J.S. Wilson, ‘On products of soluble groups of finite rank', Comment. Math. Helv. 60(1985), 337–353.
J.S. Wilson, ‘Soluble groups which are products of minimax groups', Arch. Math. (Basel) 50(1988), 193–198.
J.S. Wilson, 'soluble products of minimax groups and nearly surjective derivations', J. Pure Appl. Algebra, to appear.
J.S. Wilson, 'soluble groups which are products of groups of finite rank', to appear.
J.S. Wilson, ‘A note on products of abelian-by-finite groups', Arch. Math. (Basel), to appear.
D.I. Zajtsev, ‘Products of abelian groups', Algebra i Logika 19(1980), 150–173.
D.I. Zajtsev, ‘Nilpotent approximations of metabelian groups', Algebra i Logika 20(1981), 638–653.
D.I. Zajtsev, ‘Factorizations of polycyclic groups', Mat. Zametki 29(1981), 481–490.
D.I. Zajtsev, ‘Products of minimax groups', Groups and systems of their subgroups, Akad. Nauk Ukrain. SSSR, Inst. Mat., Kiev (1983), 15–31.
D.I. Zajtsev, ‘Itô's theorem and products of groups', Mat. Zametki 33(1983), 807–818.
D.I. Zajtsev, ‘Soluble factorized groups', Construction of groups and their subgroup characterization, Akad. Nauk Ukrain. SSSR, Inst. Mat., Kiev (1984), 15–33.
D.I. Zajtsev, ‘Itô's theorem and products of groups', Ukrain. Mat. Z. 38(1986), 427–431.
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Amberg, B. (1989). Infinite factorized groups. In: Kim, A.C., Neumann, B.H. (eds) Groups — Korea 1988. Lecture Notes in Mathematics, vol 1398. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086235
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DOI: https://doi.org/10.1007/BFb0086235
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