Subnormal subgroups of group ring units

Marciniak, Zbigniew; Sehgal, Sudarshan

doi:10.1090/S0002-9939-98-04126-4

Subnormal subgroups of group ring units
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by Zbigniew S. Marciniak and Sudarshan K. Sehgal PDF

Proc. Amer. Math. Soc. 126 (1998), 343-348 Request permission

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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