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On some properties of group rings

Published online by Cambridge University Press:  09 April 2009

G. Karpilovsky
Affiliation:
Department of Mathematics La Trobe UniversityBundoora, Victoria, 3083, Australia
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Abstract

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Let Out (RG) be the set of all outer R-automorphisms of a group ring RG of arbitrary group G over a commutative ring R with 1. It is proved that there is a bijective correspondence between the set Out (RG) and a set consisting of R(G × G)-isomorphism classes of R-free R(G × G)-modules of a certain type. For the case when G is finite and R is the ring of algebraic integers of an algebraic number field the above result implies that there are only finitely many conjugacy classes of group bases in RG. A generalization of a result due to R. Sandling is also provided.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1980

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