Lie nilpotency indices of symmetric elements under oriented involutions in group algebras

Abstract

Let G be a group and let F be a eld of characteristic dierent from 2. Denote by (FG)+ the set of symmetric elements and by U+(FG) the set of symmetric units, under an oriented classical involution of the group algebra FG. We give some lower and upper bounds on the Lie nilpotency index of (FG)+ and the nilpotency class of U+(FG).