on the lower Lie nilpotency index of a group algebra

TL;DR

This paper investigates the conditions under which the lower and upper Lie nilpotency indices of a group algebra over a field of positive characteristic are equal, specifically characterizing when they take certain values related to the characteristic.

Contribution

It establishes a precise equivalence between the lower and upper Lie nilpotency indices for group algebras in specific cases, providing new insights into their relationship.

Findings

t_{L}(KG)=k if and only if t^{L}(KG)=k for k in {5p-3, 6p-4}

Characterization of when lower and upper Lie nilpotency indices coincide

Results apply to group algebras over fields with characteristic p>0

Abstract

In this article, we show that if $KG$ is Lie nilpotent group algebra of a group $G$ over a field $K$ of characteristic $p>0$, then $t_{L}(KG)=k$ if and only if $t^{L}(KG)=k$, for $k\in\{5p-3, 6p-4\}$, where $t_{L}(KG)$ and $t^{L}(KG)$ are the lower and the upper Lie nilpotency indices of $KG$, respectively.