NILPOTENT GROUPS ACTING ON ABELIAN-GROUPS

In this paper, we study certain properties of the group ring of a nilp otent group which are related to commutativity and conjugation. We est ablish some relations involving conjugates of the elements of the grou p ring; these relations are then used to get a better understanding of torsion in abelian-by-nilpotent groups; we shall see notably that giv en 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 actual ly a subgroup of A.