Free products of abelian groups in the unit group of integral group rings
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- by Eric Jespers and Guilherme Leal PDF
- Proc. Amer. Math. Soc. 126 (1998), 1257-1265 Request permission
Abstract:
We classify finite groups $G$ which are such that the unit group of the integral group ring $\mathbf {Z}G$ has a subgroup of finite index which is a non-trivial free product of abelian groups.References
- Behnam Banieqbal, Classification of finite subgroups of $2\times 2$ matrices over a division algebra of characteristic zero, J. Algebra 119 (1988), no. 2, 449–512. MR 971143, DOI 10.1016/0021-8693(88)90069-5
- Roderick Gow and Bertram Huppert, Degree problems of representation theory over arbitrary fields of characteristic $0$. On theorems of N. Itô and J. G. Thompson, J. Reine Angew. Math. 381 (1987), 136–147. MR 918845, DOI 10.1515/crll.1987.381.136
- Roderick Gow and Bertram Huppert, Degree problems of representation theory over arbitrary fields of characteristic $0$. II. Groups which have only two reduced degrees, J. Reine Angew. Math. 389 (1988), 122–132. MR 953668, DOI 10.1515/crll.1988.389.122
- Eric Jespers, Free normal complements and the unit group of integral group rings, Proc. Amer. Math. Soc. 122 (1994), no. 1, 59–66. MR 1221725, DOI 10.1090/S0002-9939-1994-1221725-1
- Eric Jespers, Guilherme Leal, and Angel del Río, Products of free groups in the unit group of integral group rings, J. Algebra 180 (1996), no. 1, 22–40. MR 1375564, DOI 10.1006/jabr.1996.0050
- 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.
- Donald Passman, Permutation groups, W. A. Benjamin, Inc., New York-Amsterdam, 1968. MR 0237627
- Derek John Scott Robinson, A course in the theory of groups, Graduate Texts in Mathematics, vol. 80, Springer-Verlag, New York-Berlin, 1982. MR 648604
- Sudarshan K. Sehgal, Topics in group rings, Monographs and Textbooks in Pure and Applied Mathematics, vol. 50, Marcel Dekker, Inc., New York, 1978. MR 508515
- S. K. Sehgal, Units in integral group rings, Pitman Monographs and Surveys in Pure and Applied Mathematics, vol. 69, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1993. With an appendix by Al Weiss. MR 1242557
- A. D. Thomas and G. V. Wood, Group tables, Shiva Mathematics Series, vol. 2, Shiva Publishing Ltd., Nantwich; distributed by Birkhäuser Boston, Inc., Cambridge, Mass., 1980. MR 572793
Additional Information
- Eric Jespers
- Affiliation: Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, Newfoundland, Canada A1C 5S7
- MR Author ID: 94560
- 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
- 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
- © Copyright 1998 American Mathematical Society
- 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