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Subnormal Subgroups of Group Ring Units

Authors: Zbigniew S. Marciniak and Sudarshan K. Sehgal
Journal: Proc. Amer. Math. Soc. 126 (1998), 343-348
MSC (1991): Primary 16S34, 16U60
MathSciNet review: 1423318
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Abstract: Let $G$ be an arbitrary group. If $a\in \mathbb{Z}G$ satisfies $a^{2}=0$, $a\ne 0$, then the units $1+a$, $1+a^{*}$ generate a nonabelian free subgroup of units. As an application we show that if $G$ is contained in an almost subnormal subgroup $V$ of units in $\mathbb{Z}G$ then either $V$ contains a nonabelian free subgroup or all finite subgroups of $G$ are normal. This was known before to be true for finite groups $G$ only.

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Additional Information

Zbigniew S. Marciniak
Affiliation: Institute of Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warszawa, Poland

Sudarshan K. Sehgal
Affiliation: Department of Mathematical Sciences, University of Alberta, Edmonton, Canada T6G 2G1

Received by editor(s): August 11, 1996
Additional Notes: This research was supported by Canadian NSERC Grant A-5300 and Polish Scientific Grant 2P30101007
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1998 American Mathematical Society