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arXiv · 2608.30408

Lie nilpotency index of skew symmetric elements in group algebras

Zsolt Adam Balogh
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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 $*$ be the classical involution of $FG$ and let $FG^-$ be the Lie subalgebra of the skew symmetric elements with respect to $*$. In this paper, we prove that the Lie nilpotency index of $FG$ is determined by its Lie subalgebra $FG^-$, 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 $FG^-$ has also been described.

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Zsolt Adam Balogh. 2026-08-31. Lie nilpotency index of skew symmetric elements in group algebras. https://arxiv.org/abs/2608.30408

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