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 $(FG{)}^{+}$ the set of symmetric elements and by ${\mathcal{U}}^{+}(FG)$ 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 ${\mathcal{U}}^{+}(FG)$.

Some corrected typos from version v2 and problems with the bibliography