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# Trivial Units in Group Rings

Published:2000-03-01
Printed: Mar 2000
• Daniel R. Farkas
• Peter A. Linnell
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## Abstract

Let $G$ be an arbitrary group and let $U$ be a subgroup of the normalized units in $\mathbb{Z}G$. We show that if $U$ contains $G$ as a subgroup of finite index, then $U = G$. This result can be used to give an alternative proof of a recent result of Marciniak and Sehgal on units in the integral group ring of a crystallographic group.
 Keywords: units, trace, finite conjugate subgroup
 MSC Classifications: 16S34 - Group rings [See also 20C05, 20C07], Laurent polynomial rings 16U60 - Units, groups of units