Lie Solvable Group Rings

Abstract

Let K[G] denote the group ring of G over the field K. One of the interesting problems which arises in the study of such rings is to find precisely when they satisfy polynomial identities. This has been solved for char K = 0 in [1] and for char K = p > 0 in [3]. The answer is as follows. If p > 0 we say that group A is p-abelian if A', the commutator subgroup of A, is a finite p-group. Moreover, for convenience, we say A is 0-abelian if and only if it is abelian.