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

Abstract

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