Nilpotent Groups Acting on Abelian Groups
Copyright policy )Nilpotent Groups Acting on Abelian Groups
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 N on an abelian group A A , then the set of torsion elements of A A with respect to the action of N N is actually a subgroup of A A .
- Université Laval Canada
\(\omega\)-torsion elements, nilpotent group, Group rings, Nilpotent groups, Group rings of infinite groups and their modules (group-theoretic aspects), module, action, integral group ring
\(\omega\)-torsion elements, nilpotent group, Group rings, Nilpotent groups, Group rings of infinite groups and their modules (group-theoretic aspects), module, action, integral group ring
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