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Subnormal Subgroups of Group Ring Units

Authors:	Zbigniew S Marciniak Sudarshan K Sehgal

Institution:	Institute of Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warszawa, Poland ; Department of Mathematical Sciences, University of Alberta, Edmonton, Canada T6G 2G1

Abstract:	Let be an arbitrary group. If $a\in \mathbb{Z}G$ satisfies $a^{2}=0$ , $a\ne 0$ , then the units , $1+a^{*}$ generate a nonabelian free subgroup of units. As an application we show that if is contained in an almost subnormal subgroup of units in $\mathbb{Z}G$ then either contains a nonabelian free subgroup or all finite subgroups of are normal. This was known before to be true for finite groups only.

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