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Constructing free subgroups
of integral group ring units


Authors: Zbigniew S. Marciniak and Sudarshan K. Sehgal
Journal: Proc. Amer. Math. Soc. 125 (1997), 1005-1009
MSC (1991): Primary 16S34, 16U60
DOI: https://doi.org/10.1090/S0002-9939-97-03812-4
MathSciNet review: 1376998
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $G$ be an arbitrary group. It is proved that if $\mathbb {Z}G$ contains a bicyclic unit $u\ne 1$, then $\langle u,u^*\rangle $ is a nonabelian free subgroup of invertible elements.


References [Enhancements On Off] (What's this?)

  • 1. B. Hartley and P. F. Pickel, Free subgroups in the unit groups of integral group rings, Canadian Journal of Math. 32 (1980), 1342-1352. MR 82i:20008
  • 2. E. Jespers, Free normal complements and the unit group of integral group rings, Proceedings of AMS 122 (1994), 59-66. MR 94k:16058
  • 3. 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. CMP 96:08
  • 4. M. Kargapolov and Yu. Mierzljakov, Fundamentals of the theory of groups, Springer-Verlag, 1979. MR 80k:20002
  • 5. D. S. Passman, Algebraic structure of group rings, Interscience, New York, 1977. MR 81d:16001
  • 6. S. K. Sehgal, Units in integral group rings, Longman's, Essex, 1993. MR 94m:16039
  • 7. S. K. Sehgal, Topics in group rings, Marcel Dekker, 1978. MR 80j:16001

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Additional Information

Zbigniew S. Marciniak
Affiliation: Institute of Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warszawa, Poland
Email: zbimar@mimuw.edu.pl

Sudarshan K. Sehgal
Affiliation: Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
Email: s.sehgal@ualberta.ca

DOI: https://doi.org/10.1090/S0002-9939-97-03812-4
Received by editor(s): October 25, 1995
Additional Notes: The authors were supported by Canadian NSERC Grant A-5300 and Polish Scientific Grant 2P30101007.
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1997 American Mathematical Society

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