Group identities on symmetric units

Abstract

Let F be an infinite field of characteristic different from 2, G a group and * an involution of G extended by linearity to an involution of the group algebra FG. Here we completely characterize the torsion groups G for which the *-symmetric units of FG satisfy a group identity. When * is the classical involution induced from g -> g(-1), g is an element of G, this result was obtained in [ A. Giambruno, S. K. Sehgal, A. Valenti, Symmetric units and group identities, Manuscripta Math. 96 (1998) 443-461]. (C) 2009 Elsevier Inc. All rights reserved.