Free products of abelian groups

in the unit group of integral group rings

Authors:
Eric Jespers and Guilherme Leal

Journal:
Proc. Amer. Math. Soc. **126** (1998), 1257-1265

MSC (1991):
Primary 16U60, 16S34

DOI:
https://doi.org/10.1090/S0002-9939-98-04340-8

MathSciNet review:
1451810

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Abstract | References | Similar Articles | Additional Information

Abstract: We classify finite groups which are such that the unit group of the integral group ring has a subgroup of finite index which is a non-trivial free product of abelian groups.

**1.**B. Banieqbal,*Classification of finite subgroups of matrices over a division algebra of characteristic zero*, J. Algebra**119**(1988), 449-512. MR**90h:20073****2.**R. Gow and B. Huppert, Degree problems of representation theory over arbitrary fields of characteristic 0, J. reine angew. Math. 381 (1987), 136-147. MR**89b:20029****3.**R. Gow and B. Huppert, Degree problems of representation theory over arbitrary fields of characteristic 0, Part 2: Groups which have only two reduced degrees, J. reine angew. Math. 389 (1988), 122-132. MR**89i:20021****4.**E. Jespers,*Free normal complements and the unit group of integral group rings*, Proc. Amer. Math. Soc.**122(1)**(1994), 59-66. MR**94k:16058****5.**E. Jespers, G. Leal and A. del Rio,*Products of free groups in the unit group of integral group rings*, J. Algebra**180**(1996), 22-40. MR**96m:16045****6.**G. Leal and A. del Rio, Products of free groups in the unit group of integral group rings II, J. Algebra**191**(1997), 240-251. CMP**97:11****7.**D.S. Passman,*Permutation groups*, Benjamin, New York, 1968. MR**38:5908****8.**D.J.S. Robinson, A course in the theory of groups, Graduate Texts in Math. 80, Springer-Verlag, New York, 1982. MR**84k:20001****9.**S.K. Sehgal,*Topics in group rings*, Marcel Dekker, New York, 1978. MR**80j:16001****10.**S.K. Sehgal,*Units of Integral Group Rings*, Longman Scientific and Technical, Essex, 1993. MR**94m:16039****11.**A.D. Thomas and G.V. Wood, Group Tables, Shiva Publishing Limited, 1980. MR**81d:20002**

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Additional Information

**Eric Jespers**

Affiliation:
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, Newfoundland, Canada A1C 5S7

Email:
ejespers@albert.math.mun.ca

**Guilherme Leal**

Affiliation:
Instituto de Matemática, Universidade Federal do Rio de Janeiro, Rio de Janeiro RJ, Brazil

Email:
gleal@mat.dme.ufrj.br

DOI:
https://doi.org/10.1090/S0002-9939-98-04340-8

Received by editor(s):
October 7, 1996

Additional Notes:
The first named author is supported in part by NSERC grant OGP0036631, Canada.

The second named author, partially supported by CNPq, Brazil, wishes to thank the Memorial University of Newfoundland for its support and friendly atmosphere.

Communicated by:
Ronald M. Solomon

Article copyright:
© Copyright 1998
American Mathematical Society