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Class groups and automorphism groups of group rings

Published online by Cambridge University Press:  18 May 2009

Kenneth A. Brown
Affiliation:
Department of Mathematics, University of Glasgow, University Gardens, Glasgow, G12 8QW
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This paper is a sequel to [2]. A polycyclic-by-finite group G was there called dihedral free if G contains no subgroup isomorphic to 〈b, a:ba = b-1 a2 = 1〉 whose normalizer has finite index in G. It was shown in [2, Theorem F] that, if R is a commutative Noetherian domain, the group ring RG is a prime Noetherian maximal order if and only if R is integrally closed, G is dihedral free, and G has no non-trivial finite normal subgroups. Throughout, R and G will be assumed to satisfy these hypotheses. The main aim of the paper is to study the class group of the maximal order RG.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 1986

References

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