Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
Alperin, J.L.; Evens, L. Varieties and elementary abelian groups. J. Pure Appl. Algebra 26(1982), 221–227. MR84a:20057
Artin, E. The orders of the classical simple groups. Comm. Pure Appl. Math. 8(1955), 455–472. MR17, 457
Aschbacher, M: Guralnick, R. Some applications of the first cohomology group. J. Algebra 90(1984), 446–460.
Avrunin, G.S.; Scott, L.L. Quillen stratification for modules. Invent.Math. 66(1982), 277–286. MR83h:20048
Banaschewski, B. Integral group rings of finite groups. Canad. Math. Bull. 10(1967), 635–642. MR38 1187
deBarros, L.G.X. O problema do isomorfismo para álgebra de grupo. Master’s thesis, Univ. de São Paulo, 1974.
Bass, H. The stable structure of quite general linear groups. Bull. Amer. Math. Soc. 70(1964), 429–433. MR28 4035
Bass, H. Algebraic K-theory. W.A. Benjamin, New York, MR40 2736
Baumslag, G. (ed.) Reviews on Infinite Groups. Amer. Math. Soc., Providence, R.I. 1974. MR50 2311
Bautista Ramos, R. Algunos resultados sobre álgebras de grupos abelianos finitos. An. Inst. Mat. Univ. Nac. Autónoma México 7(1967), 1–25. MR38 2220
Bautista Ramos, R. Errata: Algunos resultados sobre álgebras de grupos abelianos finitos. An. Inst. Mat. Univ. Nac. Autónoma México 8(1968), 79. MR39 5712
Beers, D.; Richman, F.; Walker, E.A. Group algebras of Abelian groups. Rend. Sem. Mat. Univ. Padova 69(1983), 41–50. Zbl.522.20006
Benson, D. Modular Representation Theory: New Trends and Methods. Lecture Notes in Math., 1081, Springer, Berlin, 1984.
Berman, S.D. On certain properties of integral group rings. (Russian) Dokl. Akad. Nauk SSSR (N.S.) 91 (1953), 7–9. MR15,99
Berman, S.D. On a necessary condition for isomorphism of integral group rings. (Ukrainian) Dopovīdī Akad. Nauk Ukraïn. RSR 1953, 313–316. MR15,599
Berman, S.D. On the equation xm=1 in an integral group ring. (Russian) Ukrain. Mat. Zh. 7(1955), 253–261. MR17,1048
Berman, S.D. On automorphisms of the centre of an integral group ring. (Russian) Dokl. Soobsch. Uzhgorod. Gos. Univ. Ser. Fiz.-Mat. Nauk 1960, no.3, 55.
Berman, S.D. (Review of Cohn-Livingstone 1963). RZh Mat. 1964, vol. 10, p.26.
Berman, S.D.; Rossa, A.R. Integral group rings of finite and periodic groups. (Russian), Algebra and Math. Logic: Studies in Algebra, pp. 44–53, Izdat. Kiev. Univ., Kiev, 1966. MR35 265
Beyl, F. Rudolf; Tappe, Jürgen. Group Extensions, Representations and the Schur Multiplicator. Lecture Notes in Math., 958, Springer, Berlin, 1982. MR84f:20002
Boerner, Hermann. Enzyklopädie der mathematischen Wissenschaften mit Einschluss ihrer Anwendungen, Band I: Algebra und Zahlentheorie. 1. Teil A. Grundlagen; B. Algebra. Heft 6, Teil II. No. 15: Darstellungstheorie der endlichen Gruppen. B.G. Teubner, Stuttgart, 1967. MR37 2872
Bovdi, A.A. On group rings of nilpotent groups. (Russian) Twelfth All-Union Algebra Colloquium (Sverdlovsk, 1973), Abstracts of papers, Part I, p.130, Akad. Nauk SSSR Ural Nauchn. Centre., Sverdlovsk, 1973. See MR58 15767a
Bovdi, A.A. Group Rings. Textbook. (Russian), University publishers, Uzhgorod, 1974, Zbl.339.16004
Bovdi, A.A. Remarks on the automorphisms of a group ring. (Russian) Latv. Mat. Ezhegodnik 18(1976), 19–26. MR58 5760
Bovdi, A.A. The structure of group bases of a group ring. (Russian) Mat. Zametki 32(1982), 459–468. = Math. Notes 32(1982), 709–713. MR84e:20010
Bovdi, A.A.; Patai, Z.F. The structure of the centre of the multiplicative group of the group ring of a p-group over a ring of characteristic p. (Russian) Vestsī Akad. Navuk BSSR Ser. Fīz.-Mat. Navuk 1978, no.1, 5–11. MR58 5762
Bovdi, A.A.; Semirot, M.C. Involution and isomorphism of group rings. (Russian) Twelfth All-Union Algebra Colloquium (Sverdlovsk, 1973), Abstracts of papers, Part I, p.131, Akad. Nauk SSSR Ural Nauchn. Centr., Sverdlovsk, 1973. See MR58 15767a
Bovdi, A.A.; Semirot, M.C. On the question of the isomorphism of modular group algebras. (Ukrainian) Abstracts. Second Conf. of Young Scientists Akad. Nauk UkSSR, pp.48–54, Uzhgorod, 1975 (dep VINITI, No.1734–76) RZhMat1976, 9A293.
The following papers of Brauer are reproduced in Vols. I and II of: Richard Brauer: Collected Papers. MIT Press, Cambridge MA, 1980. MR8li:01017
Brauer, R. Über Systeme hyperkomplexer Zahlen. Math. Z. 30 (1929), 79–107. F.d.M.55II, 88.
Brauer, R. On modular and p-adic representations of algebras. Proc. Nat. Acad. Sci. U.S.A. 25(1939), 252–258. Zbl.22,303
Brauer, R. Zur Darstellungstheorie der Gruppen endlicher Ordnung. Math. Z. 63 (1956), 406–444. MR17,824
Brauer, R. Number theoretical investigations on groups of finite order. Proceedings of the international symposium on algebraic number theory, Tokyo & Nikko, 1955, pp.55–62. Science Council of Japan, Tokyo, 1956. MR18, 716
Brauer, R., Representations of finite groups. Lectures on Modern Mathematics, Vol. I, pp.133–175, Wiley, New York, 1963, MR31 2314
Brown, C.F. Automorphisms of integral group rings. Ph.D. thesis, Michigan State Univ., 1971. DAI32(1972), p.5302B
Carlson, J.F. Periodic modules over modular group algebras. J. London Math. Soc. (2)15(1977), 431–436. MR57 12664
Cliff, G.H.; Sehgal, S.K.; Weiss, A.R. Units of integral group rings of metabelian groups. J. Algebra 73 (1981), 167–185. MR83i:20006
Cohen, D.E. On abelian group algebras. Math. Z. 105(1968), 267–268. MR37 4176
Cohn, J.A.; Livingstone, D. On groups of the order p3. Canad. J. Math. 15(1963), 622–624. MR27 3700
Cohn, J.A.; Livingstone, D. On the structure of group algebras. I. Canad. J. Math. 17(1965), 583–593. MR31 3514.
Cohn, J.A.; Livingstone, D. On the structure of group algebras. II. Unpublished, 196x.
Cohn, P.M. Integral modules, Lie-rings and free groups. Ph.D. thesis, Cambridge Univ., 1951.
Cohn, P.M. Generalization of a theorem of Magnus. Proc. London Math. Soc. (3)2(1952), 297–310. Corrigenda: see index page. MR14,532
Coleman, D.B. Finite groups with isomorphic group algebras. Ph.D. thesis, Purdue Univ., 1961. DA22(1962), p.2405
Coleman, D.B. Finite groups with isomorphic group algebras. Trans. Amer. Math. Soc. 105(1962), 1–8. MR26 191
Coleman, D.B. On the modular group ring of a p-group. Proc. Amer. Math. Soc. 15(1965), 511–514. MR29 2306
Crowell, R.H. Corresponding group and module sequences. Nagoya Math. J. 19(1961), 27–40. Zbl.101,264
Culler, M. Homology equivalent finite groups are isomorphic. Proc. Amer. Math. Soc. 72(1978), 218–220. MR58 5971
Curtis, Charles W.; Reiner. Irving. Representation Theory of Finite Groups and Associative Algebras. Interscience-Wiley, New York, 1962. MR26 2519
Curtis, C.W.; Reiner, I. Methods of Representation Theory. Vol. I. Wiley, New York, 1981. MR82i:20001
Dade, E.C. Answer to question of R. Brauer. J. Algebra I(1964), 1–4. MR30 1191
Dade, E.C. Deux groupes finis distincts ayant la même algèbre de groupe sur tout corps. Math. Z. 119(1971), 345–348. MR43 6329
Dennis, R.K. The structure of the unit group of group rings. Ring theory, II, pp.103–130, Dekker, New York, 1977. MR56 3047
Deskins, W.E. On finite Abelian groups having isomorphic group algebras. Bull. Amer. Math. Soc. 61(1955), 125.
Deskins, W.E. Finite abelian groups with isomorphic group algebras. Duke Math J. 23(1956), 35–40. MR17,1052
Dickson, L.E. Linear Groups. B.G. Teubner, Leipzig, 1901; Dover, New York, 1958. MR21 3488 F.d.M.32, 128
Dieckmann, E.M. Isomorphism of group algebras of p-groups. Ph.D. thesis, Washington Univ., 1967. DA28(1968), p.4194B–4195B
Dieudonné, J. Lie groups: classical, algebraic and formal. Lecture, 21-st British Mathematical Colloquium, Birmingham, 28 March 1969.
Endo, S.; Miyata, T.; Sekiguchi, K. Picard groups and automorphism groups of integral group rings of metacyclic groups. J. Algebra 77(1982), 286–310. MR84b:16010
Evens, L. The cohomology ring of a finite group. Trans. Amer. Math. Soc. 101(1961), 224–239. MR25 1191
Fröhlich, A. The Picard group of non-commutative rings, in particular of orders. Trans. Amer. Math. Soc. 180(1973), 1–45. MR47 6571
Furukawa, T. A note on isomorphisminvariants of a modular group algebra. Math. J. Okayama Univ. 23(1981), 1–5. MR82k:16012
Furukawa, T. On isomorphism invariants of integral group rings. Math. J. Okayama Univ. 23(1981), 125–130. MR83d:20004
Gallagher, P.X. Invariants for finite groups. Adv. in Math. 34(1979), 46–57. MR81c:20011
Garrison, S.C. Determining the Frattini subgroup from the character tables. Canad. J. Math. 28(1976), 560–567. MR53 8214
Gilmer, R. Commutative Semigroup Rings. U. Chicago Press, Chicago, 1984.
Gorenstein, D. (ed.) Reviews on Finite Groups. Amer. Math. Soc., Providence, 1974. MR50 2312
Gorenstein, D.; Lyons, R. The local structure of finite groups of characteristic 2 type. Mem. Amer. Math. Soc. 42(1983), no.276. MR84g:20025
Green, J.A. Richard Dagobert Brauer. Bull. London Math. Soc. 10(1978), 317–342. MR80g:01024
Gruenberg, K.W. Some Cohomological Topics in Group Theory. Queen Mary College, London, 1967. MR41 3608
Gruenberg, K.W. Cohomological Topics in Group Theory. Lecture Notes in Math., 143, Springer, Berlin, 1970. MR43 4923
Gruenberg, K.W.; Roggenkamp, K.W. Decomposition of the augmentation ideal and of the relation modules of a finite group. Proc. London Math. Soc. (3)31(1975), 149–166. MR51 10447
Gruenberg, K.W.; Roggenkamp, K.W. The decomposition of relation modules: a correction. Proc. London Math. Soc. (3)45(1982), 89–96. MR83j:20019
Grunewald, F.; Segal, D. Some general algorithms. I: Arithmetic groups. Ann. of Math.(2)112(1980), 531–583. MR82d:20048a
Hall, M.; Senior, J. The Groups of Order 2n(n⩽6). Macmillan, New York, 1964. MR29 5889
Hall, Philip. The classification of prime power groups. J. Reine Angew. Math. 182 (1940), 130–141. MR2,211
Hashisaki, J. On group algebras of prime power groups. Ph.D. thesis, Univ. Illinois, Urbana, 1953. DA13(1953), p.1211
Hattori, Akira. On the isomorphism problem of group algebras. (Japanese) Lecture, Algebra Colloquium No.25. Tokyo, 5 June, 1971.
Hattori, Akira. Strong separability and group algebras. Sci. Papers College Arts Sci. Univ. Tokyo 35(1985)
Hawkins, T. New light on Frobenius’ creation of the theory of group characters. Arch. Hist. Exact Sci. 12(1974), 217–243. MR56 5161
Higman, G. The units of group-rings. Proc. London Math. Soc. (2)46(1940),231–248. MR2,5
Higman, G. Units in group rings. D. Phil. thesis, Oxford Univ., 1940.
Hoheisel, G. Über Charaktere. Monatsh. Math. Phys. 48(1939), 448–456. MR1,104
Holvoet, R. Sur les Z2-algèbres du groupe diédral d’ordre 8 et du groupe quaternionique. C.R. Acad. Sci. Paris Sér.A–B 262(1966), A209–A210. MR32 5726
Holvoet, R. Sur l’isomorphie d’algèbres de groupes. Bull. Soc. Math. Belg. 20(1968), 264–282. MR39 1571
Holvoet, R. De groepalgebra van een eindige p-groep over een veld met karakteristiek p. Simon Stevin 42(1969), 157–170. MR40 4382
Hooke, R. Finite groups and restricted Lie algebras. Duke Math. J. 8(1941), 533–540. MR3,103
Hughes, I.; Pearson, K.R. The group of units of the integral group ring ZS3. Canad. Math. Bull. 15(1972), 529–534. MR48 4089
Hughes, I.; Wei, C.-H. Group rings with only trivial units of finite order. Canad. J. Math. 24(1972), 1137–1138. MR47 313
Huppert, B. Endliche Gruppen. I. Springer, Berlin, 1967. MR37 302
Huppert, B.; Blackburn, N. Finite Groups. II. Springer, Berlin, 1982. MR84i:20001a
Isaacs, I.M. Character Theory of Finite Groups. Academic Press, New York, 1976. MR57 417
Jackson, D.A. The groups of units of the integral group rings of finite metabelian and finite nilpotent groups. Quart. J. Math. Oxford Ser. (2)20(1969), 319–331. MR40 2766.
Jacobson, N. Classes of restricted Lie algebras of characteristic p, II. Duke Math. J. 10(1943), 107–121. MR4,187
Jennings, S.A. The structure of the group ring of a p-group over a modular field. Trans. Amer. Math. Soc. 50(1941), 175–185. MR3,34
Johnson, D.L. The modular group-ring of a finite p-group. Proc. Amer. Math. Soc. 68(1978), 19–22. MR56 15744
Karpilovsky, G. On group rings of finite metabelian groups. J. Austral. Math. Soc. Ser.A 28(1979), 378–384. MR82j:20015
Karpilovsky, G. On certain group ring problems. Bull. Austral. Math. Soc. 21(1980), 329–350. MR82c:16011
Karpilovsky, G. On some properties of group rings. J. Austral. Math. Soc. Ser.A 29(1980), 385–392. MR81h:16023
Karpilovsky, G. Finite groups with isomorphic group algebras. Illinois J.Math.25(1981), 107–111. MR82d:20010
Karpilovsky, G. On some properties of group rings. Publ. Math. Debrecen 29(1982), 101–105. MR83m:16010
Karpilovsky, G. Commutative Group Algebras. M. Dekker, New York, 1983. MR85a:16014
Kawada, Yukiyosi. On the group ring of a topological group. Math. Japon. 1(1948), 1–5. MR10,11
Keast, G.D. The group of units of the integral group ring ZA4. M.Sc. thesis, La Trobe Univ. 1975.
Kmet, S.; Sehgal, S. Some isomorphism invariants of integral group rings. Rocky Mountain J. Math. (198x)
Koshitani, S. On the nilpotency indices of the radicals of group algebras of P-groups which have cyclic subgroups of index P. Tsukuba J. Math. 1(1977), 137–148. MR58 773
Lam, S.P. Unstable algebras over the Steenrod algebra and cohomology of classifying spaces. Ph.D. thesis, Cambridge Univ., 1982.
Lam, S.P. Unstable algebras over the Steenrod algebra. Algebraic Topology, Aarhus 1982, pp.374–392. Lecture Notes in Math., 1051, Springer, Berlin, 1984.
Laudal, O.A. p-groups and Massey products. Preprint Series 1975/76 No. 30 (revised Jan. 1977), Matematisk Institut, Aarhus Univ., 1976. RZh1977,5A276
Lazard, M. Sur les groupes nilpotents et les anneaux de Lie. Ann. Sci. Ecole Norm. Sup. (3)71(1954), 101–190. MR19,529
Lazard, M. Groupes analytiques p-adiques. Inst. Hautes Études Sci. Publ. Math. No.26 (1965), 389–603. MR35 188
Learner, A. Cohomology of Groups. Queen Mary College, London, 1965.
Lombardo-Radice, L. Intorno alle algebre legate ai gruppi di ordine finito. Nota 1a, Rend. Sem. Mat. Roma (4)2(1938), 312–322. Zbl.20,341.
Losey, G. On dimension subgroups. Trans. Amer. Math. Soc. 97(1960), 474–486. MR26 6260
Makasikis, A. Sur l’isomorphie d’algèbres de groupes sur un champ modulaire. Bull. Soc. Math. Belg. 28(1976), 91–109. MR81b:20009
Mehrvarz, A.A. Topics in the isomorphism of group rings. Ph.D. thesis, Stirling Univ., 1979.
Merklen, H.A. Group bases of group rings. Bol. Soc. Brasil. Mat. 10(1979), 15–23. MR82d:20011
Morand, R. Une propriété des algèbres de groupes nilpotentes finis. C.R. Acad. Sci. Paris Sér. A-B 272(1971), A1227–A1229. MR43 7524
Motose, K. On a theorem of S. Koshitani. Math. J. Okayama Univ. 20(1978), 59–65. MR58 10995
Müller, W. Gruppenalgebren über nichtzyklischen p-Gruppen. I. Die Dieder-und die Quasidiedergruppen. J. Reine Angew. Math. 266(1974), 10–48. MR49 5150.
Müller, W. Gruppenalgebren über nichtzyklischen p-Gruppen. II: Die Quaternionengruppe und die verallgemeinerten Quaternionengruppen. J. Reine Angew. Math. 267(1974), 1–19. MR49 9064
Nachev, N.A.; Mollov, T.Zh. Ulm-Kaplansky invariants of the group of normed units of the center of the group ring of an FC-p-group over a commutative ring of characteristic p. (Russian) Serdica 7(1981), 42–56. MR82k:20015
Nachev, N.A.; Mollov, T.Zh. An isomorphism of modular group algebras of finite 2-groups for which the factor-group with respect to the center has order four. (Russian) C.R. Acad. Bulgare Sci. 34(1981), 1633–1636. MR83m:20013
Nagao, H. On the groups with the same table of characters as symmetric groups. J. Inst. Polytech. Osaka City Univ. Ser. A. 8(1957), 1–8. MR19,387
Neroslavskii, O.M. Structures that are connected with radical rings. (Russian) Vestsī Akad. Navuk BSSR Ser. Fīz.-Mat. Navuk 1973, no. 2, 5–10. MR48 8547
Obayashi, T. Solvable groups with isomorphic group algebras. J. Math. Soc. Japan 18(1966), 394–397. MR33 5750.
Obayashi, T. On integral group rings. (Japanese) Sûgaku 19(1967), 82–94. MR37 4178
Obayashi, T. Integral group rings of finite groups. Osaka J. Math. 7(1970), 253–266. MR43 2122
Obayashi, T. On the isomorphism problem. (Japanese) Proceedings, 20-th Symposium on Algebra, pp.45–52, Japan, 1974.
Obayashi, T. A note on group bases for integral group rings. Unpublished, 1978.
Pahlings, H. Characterization of groups by their character tables I. Comm. Algebra 4(1976), 111–153. MR53 8217
Parmenter, M.M. Dimension theory, isomorphism and related problems in group rings. Ph.D. thesis, Univ. of Alberta, 1972.
Parmenter, M.M.; Polcino Milies, C. A note on isomorphic group rings. Bol. Soc. Brasil. Mat. 12(1981), 57–59. MR84c:20015
Passi, I.B.S.; Sehgal, S.K. Isomorphism of modular group algebras. Math. Z. 129(1972), 65–73. MR47 314
Passi, I.B.S. Group Rings and Their Augmentation Ideals. Lecture Notes in Math., 715, Springer, Berlin, 1979. MR80k:20009
Passman, D.S. Group ring properties of groups. Ph.D. thesis, Harvard Univ., 1964.
Passman, D.S. Isomorphic groups and group rings. Pacific J. Math. 15(1965), 561–583. MR33 1381
Passman, D.S. The group algebras of groups of order p4 over a modular field. Michigan Math. Journal 12(1965), 405–415. MR32 2492
Passman, D.S. Corrections to: "Isomorphic groups and group rings". Pacific J. Math 43(1972), 823–824. MR48 398
Passman, D.S. Advances in group rings. Israel J. Math. 19(1974), 67–107. MR50 9945
Passman, D.S. The Algebraic Structure of Group Rings. Wiley-Interscience, New York, 1977. MR81d:16001
Passman, D.S.; Smith, P.F. Units in integral group rings. J. Algebra 69(1981), 213–239. MR82h:20009
Perlis, S.; Walker, G.L. Finite Abelian group algebras. I. Bull. Amer. Math. Soc. 54(1948), 651.
Perlis, S.; Walker, G.L. Abelian group algebras of finite order. Trans. Amer. Math. Soc. 68(1950), 420–426. MR11,638
Peterson, G.L. On the automorphism group of an integral group ring. Ph.D. thesis, Michigan State Univ., 1975. DAI36(1975), p.1260B–1261B
Peterson, G.L. Automorphisms of the integral group ring of Sn. Proc. Amer. Math. Soc. 59(1976), 14–18. MR54 385.
Peterson, G.L. On the automorphism group of an integral group ring, I. Arch. Math. (Basel) 28(1977), 577–583. MR57 3184a
Peterson, G.L. On the automorphism group of an integral group ring, II. Illinois J. Math. 21(1977), 836–844. MR57 3184b
Polcino Milies, F.C. Anéis de Grupos. Instituto de Matemática e Estatistica, Univ. de São Paulo, São Paulo, 1976. Zbl.407.16008
Quillen, D.G. On the associated graded ring of a group ring. J. Algebra 10(1968), 411–418. MR38 245
Quillen, D. The spectrum of an equivariant cohomology ring: I. Ann. of Math. (2)94(1971), 549–572. MR45 7743
Quillen, D. The spectrum of an equivariant cohomology ring: II. Ann. of Math. (2)94(1971), 573–602. MR45 7743
Quillen, D. A cohomological criterion for p-nilpotence. J. Pure Appl. Algebra 1(1971), 361–372. MR47 6886
Quillen, D.; Venkov, B.B. Cohomology of finite groups and elementary abelian subgroups. Topology 11(1972), 317–318. MR45 3576
Rector, D.L. Noetherian cohomology rings and finite loop spaces with torsion. J. Pure Appl. Algebra 32(1984), 191–217.
Reiner, I.; Roggenkamp, K.W. Integral representations. Lecture Notes in Math., 744, Springer, Berlin, 1979. MR80k:20010
Rieffel, M.A. A characterization of the group algebras of the finite groups. Pacific J. Math. 16(1966), 347–363. MR32 2493
Ritter, J. On a Zassenhaus conjecture about units in group rings. Lecture, Orders and Their Applications, Oberwolfach, 7 June 84.
Ritter, J.; Sehgal, S. Isomorphism of group rings. Arch. Math. (Basel) 40(1983), 32–39. MR84k:16015
Roggenkamp, K.W. Units in metabelian integral grouprings. I. Jackson’s unit theorem revisited. Quart. J. Math. Oxford Ser. (2) 32(1981), 209–224. MR82i:16009
Roggenkamp, K.W. The isomorphism problem and units in group rings of finite groups. Groups — St. Andrews 1981, pp.313–327, Cambridge Univ. Press, Cambridge, 1982. MR84m:20017
Roggenkamp, K.W. Automorphisms and isomorphisms of integral group rings of finite groups. Groups-Korea 1983, pp.118–135, Lecture Notes in Math., 1098, Springer, Berlin, 1984.
Roggenkamp, K.W. Isomorphisms of p-adic group rings I. Lecture, Orders and Their Applications, Oberwolfach, 4 June 84.
Roggenkamp, K.W.; Scott, L. Non-splitting examples for normalized units in integral group rings of metacyclic Frobenius groups. C.R. Math. Rep. Acad. Sci. Canada 3(1981), 29–32. MR82b:20009
Roggenkamp, K.W.; Scott, L.L. Units in metabelian group rings: non-splitting examples for normalized units. J. Pure Appl. Algebra 27 (1983), 299–314. Zbl.509.16006
Roggenkamp, K.W.; Scott, L.L. Units in metabelian group rings: non-splitting examples for normalized units. Addendum. J. Pure Appl. Algebra 28(1983), 109. Zbl.509.16006
Roggenkamp, K.W.; Scott, L.L. Units in group rings: Splittings and the isomorphism problem. To appear, 1985.
Röhl, F. On induced isomorphisms of group rings. Groups-Korea 1983, pp. 136–141, Lecture Notes in Maths., 1098, Springer, Berlin, 1984.
Röhl, F. On graded algebras associated to isomorphic modular group algebras. To appear, 198x.
Roitman, M. A complete set of invariants for finite groups and other results. Adv. in Math. 41(1981), 301–311. MR83c:20009
Rosenberg, A.; Zelinsky, D. Automorphisms of separable algebras. Pacific J. Math. 11(1961), 1109–1117. MR26 6215
Rossa, A.R. Group rings of p-groups over the ring of integral p-adic numbers. (Russian) Sibirsk. Mat. Zh. 9(1968), 220–222. MR36 6514
Saksonov, A.I. Certain integer-valued rings associated with a finite group. (Russian) Dokl. Akad. Nauk SSSR 171(1966), 529–532. = Soviet Math. Dokl. 7(1966), 1513–1516. MR34 7676
Saksonov, A.I. The integral ring of characters of a finite group. (Russian) Vestsī Akad. Navuk BSSR Ser. Fīz.-Mat. Navuk 1966, no.3, 69–76. MR35 269
Saksonov, A.I. On group rings of finite p-groups over certain integral domains. (Russian) Dokl. Akad. Nauk BSSR 11(1967), 204–207. MR35 270
Saksonov, A.I. Group-algebras of finite groups over a number field. (Russian) Dokl. Akad. Nauk BSSR 11(1967), 302–305. MR35 1681
Saksonov, A.I. Group rings of finite groups. I. (Russian) Publ. Math. Debrecen 18 (1971), 187–209. MR46 5425
Saksonov, A.I. Group rings of finite groups. II. (Russian) Publ. Math. Debrecen 19 (1972), 65–86 (1973). MR48 2238
Sandling, R. Note on the integral group ring problem. Math. Z. 124(1972), 255–258. MR45 3594
Sandling, R. Group rings of circle and unit groups. Math. Z. 140(1974), 195–202. MR52 3217
Sandling, R. Graham Higman’s thesis "Units in group rings". Integral Representations and Applications, pp.93–116, Lecture Notes in Math., 882, Springer, Berlin, 1981. MR83g:20009
Sandling, R. Computer calculations of units in modular group algebras. Lecture, Orders and Their Applications, Oberwolfach, 8 June 84.
Sandling, R. Units in the modular group algebra of a finite abelian p-group. J. Pure Appl. Algebra 33(1984), 337–346.
Scharlau, W. Quadratic and Hermitian Forms. Springer, Berlin, 1985.
Scott, L.L. Isomorphisms of p-adic group rings. II. Lecture, Orders and Their Applications, Oberwolfach, 5 June 84.
Sehgal, Sudarshan K. On the isomorphism of group algebras. Math. Z. 95(1967), 71–75. MR34 5950
Sehgal, S.K. On the isomorphism of integral group rings. I. Canad. J. Math. 21(1969), 410–413. MR41 366
Sehgal, S.K. On the isomorphism of integral group rings. II. Canad. J. Math. 21(1969), 1182–1188. MR42 392
Sehgal, S.K. Isomorphism of p-adic group rings. J. Number Theory 2(1970), 500–508. MR42 1917
Sehgal, S.K. Topics in Group Rings. Dekker, New York, 1978. MR80j:16001
Sehgal, Sudarshan K.; Sehgal, Surinder K.; Zassenhaus, Hans J. Isomorphism of integral group rings of abelian by nilpotent class two groups. Comm. Algebra 12(1984), 2401–2407.
Sekiguchi, Katsusuke. On the units of integral group rings. Tokyo J. Math. 3(1980), 149–162. MR81k:20010
Serre, J.-P. Arithmetic groups. Homological Group Theory, pp.105–136, Cambridge Univ. Press, Cambridge, 1979. MR82b:22021
Small, L.W. (ed.). Reviews in Ring Theory. Amer. Math. Soc., Providence, 1981.
Smith, S.D. (Review of Isaacs 1976). Math. Rev. 57(1979), 60
Speiser, A., Die Theorie der Gruppen von endlicher Ordnung. Zweite Auflage. Springer, Berlin, 1927. F.d.M.53,104
Stallings, J. Homology and central series of groups. J. Algebra 2(1965), 170–181. MR31 232
Steinberg, R. Lectures on Chevalley Groups. Yale Univ., New Haven, 1968. MR57 6215
Takahashi, Shuichi. A characterization of group rings as a special class of Hopf algebras. Canad. Math. Bull. 8(1965), 465–475. MR32 2479
Takahashi, Shuichi. Anneaux tordus de groupes comme des anneaux de Hilbert. J. Algebra 20(1972), 161–166. MR44 2852
Thrall, R.M. Conference on Algebra, Univ. Michigan, 25–28 July 1947.
Valenza, R.J. Strongly determined subgroups. Comm. Algebra 9(1981), 669–677. MR82c:20012
Ward, H.N. Some results on the group algebra of a group over a prime field. Seminar on Finite Groups and Related Topics, pp.13–19. Mimeographed notes, Harvard Univ., 1960–1961.
Weidman, D.R. The character ring of a finite group. Illinois J. Math. 9(1965), 462–467. MR31 1298
Weil, A. Algebras with involutions and the classical groups. J. Indian Math. Soc. (N.S.)24(1960), 589–623. MR25 147
Weller, W.R. The units of the integral group ring ZD4. D.Ed. thesis, Pennsylvania State Univ., 1972. DAI33(1973),p.4921B
Whitcomb, A. The group ring problem. Ph.D. thesis, Univ. of Chicago, 1968.
Yap, W.-L. On the isomorphism problem for group rings. Master’s thesis, Queen’s Univ., Kingston, Ontario, 1972.
Yu, C.-Y. Group rings over modular fields. Ph.D. thesis, Pennsylvania State Univ., 1970. DAI32(1972),p.446B
Zalesskii, A.E.; Mihalev, A.V. Group rings. (Russian) Current problems in mathematics, Vol.2, pp.5–118, Akad. Nauk SSSR VINITI, Moscow, 1973. = J. Soviet Math. 4(1975), 1–78. MR54 2723
Zassenhaus, H. Ein Verfahren, jeder endlichen p-Gruppe einen Lie-Ring mit der Charakteristik p zuzuordnen. Abh. Math. Sem. Hansische Univ. 13(1939), 200–207. Zbl.21.200
Zassenhaus, H. On the torsion units of finite group rings. Estudos de matemática em homenagem ao Prof. A. Almeida Costa, pp.119–126. Instituto de Alta Cultura, Lisbon, 1974. MR51 12922
Zassenhaus, H. On A-group rings. Lecture, Orders and Their Applications, Oberwolfach, 6 June 84.
Zhmud’, È.M. On kernels of homomorphisms of linear representations of finite groups. (Russian) Mat. Sb.(N.S.)44(86)(1958),353–408. MR20 5236
Zhmud’, È.M.; Kurennoi, G.Ch. The finite groups of units of an integral group ring. (Russian) Vestnik Har’kov. Gos. Univ. 1967, no.26, 20–26. MR40 2770
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1985 Springer-Verlag
About this paper
Cite this paper
Sandling, R. (1985). The isomorphism problem for group rings: A survey. In: Reiner, I., Roggenkamp, K.W. (eds) Orders and their Applications. Lecture Notes in Mathematics, vol 1142. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074806
Download citation
DOI: https://doi.org/10.1007/BFb0074806
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-15674-1
Online ISBN: 978-3-540-39601-7
eBook Packages: Springer Book Archive