Unit groups of integral group rings

Bist, Vikas

doi:10.1090/S0002-9939-1994-1156464-9

Unit groups of integral group rings
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by Vikas Bist PDF

Proc. Amer. Math. Soc. 120 (1994), 13-17 Request permission

Abstract:

Let $U(\mathbb {Z}G)$ be the unit group of the integral group ring $\mathbb {Z}G$. A group $G$ satisfies $({\ast })$ if either the set $T(G)$ of torsion elements of $G$ is a central subgroup of $G$ or, otherwise, if $x \in G$ does not centralize $T(G)$, then for every $t \in T(G), {x^{ - 1}}tx = {t^{ - 1}}$. This property appears quite frequently while studying $U(\mathbb {Z}G)$. In this paper we investigate why one encounters this property and we have also given a "unified proof" for some known results regarding this property. Further, some additional results have been obtained.

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