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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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: 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.


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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