Nilpotency of group ring units symmetric with respect to an involution

Let F be an infinite field of characteristic different from 2. Let G be a torsion group having an involution *, and consider the units of the group ring F G that are symmetric with respect to the induced involution. We classify the groups G such that these symmetric units satisfy a nilpotency identity (x1, ..., xn) = 1. © 2009 Elsevier B.V. All rights reserved