Lie nilpotency index of skew symmetric elements in group algebras

Abstract

Let $FG$ be the group algebra of a finite $p$-group $G$ over a finite field $F$ of characteristic $p$, where $p$ is an odd prime. Let $\ast$ be the classical involution of $FG$ and let $F{G}^{-}$ be the Lie subalgebra of the skew symmetric elements with respect to $\ast$. In this paper, we prove that the Lie nilpotency index of $FG$ is determined by its Lie subalgebra $F{G}^{-}$, in the case when $G$ is a $p$-group with a commutator subgroup of order $p$. The structure of the terms of the lower Lie central series of $F{G}^{-}$ has also been described.

arXiv commentAccepted for publication in Carpathian Mathematical Publications