Subnormal Subgroups of Group Ring Units
Proc. Amer. Math. Soc. 126 (1998), 343-348.

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

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

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.