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Lie nilpotency indices of symmetric elements under oriented involutions in group algebras (1209.6256v3)
Published 27 Sep 2012 in math.RA and math.GR
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 $\mathcal{U}+(FG)$.