Nilpotent groups acting on abelian groups
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- by Charles Cassidy and Guy Laberge PDF
- Proc. Amer. Math. Soc. 119 (1993), 697-700 Request permission
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 $A$.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 119 (1993), 697-700
- MSC: Primary 20C07
- DOI: https://doi.org/10.1090/S0002-9939-1993-1185258-2
- MathSciNet review: 1185258