Subnormal subgroups of group ring units
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- by Zbigniew S. Marciniak and Sudarshan K. Sehgal
- Proc. Amer. Math. Soc. 126 (1998), 343-348
- DOI: https://doi.org/10.1090/S0002-9939-98-04126-4
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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.References
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Bibliographic 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, Canada T6G 2G1
- MR Author ID: 158130
- Email: S.Sehgal@ualberta.ca
- 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
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 343-348
- MSC (1991): Primary 16S34, 16U60
- DOI: https://doi.org/10.1090/S0002-9939-98-04126-4
- MathSciNet review: 1423318