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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Unit groups of integral group rings


Author: Vikas Bist
Journal: Proc. Amer. Math. Soc. 120 (1994), 13-17
MSC: Primary 16U60; Secondary 16S34, 20C05
DOI: https://doi.org/10.1090/S0002-9939-1994-1156464-9
MathSciNet review: 1156464
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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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DOI: https://doi.org/10.1090/S0002-9939-1994-1156464-9
Article copyright: © Copyright 1994 American Mathematical Society