Nilpotency Indices of Symmetric Elements of Group Algebras

Let G be a group and let F be a field of characteristic different from 2. Denote by (FG)+ the set of symmetric elements and by U +(FG) the set of symmetric units of the group algebra FG, with respect to the canonical involution on FG sending each group element to its inverse. In this article, we give some lower and upper bounds on the Lie nilpotency index of (FG)+ and the nilpotency class of U +(FG); furthermore, we classify the groups for which these bounds are achieved.