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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Nilpotent groups acting on abelian groups


Authors: Charles Cassidy and Guy Laberge
Journal: Proc. Amer. Math. Soc. 119 (1993), 697-700
MSC: Primary 20C07
MathSciNet review: 1185258
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Abstract: In this paper, we study certain properties of the group ring of a nilpotent group which are related to commutativity and conjugation. We establish some relations involving conjugates of the elements of the group ring; these relations are then used to get a better understanding of torsion in abelian-by-nilpotent groups; we shall see notably that given any action of a nilpotent group $ N$ on an abelian group $ A$, then the set of torsion elements of $ A$ with respect to the action of $ N$ is actually a subgroup of $ A$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1185258-2
PII: S 0002-9939(1993)1185258-2
Article copyright: © Copyright 1993 American Mathematical Society