on the lower Lie nilpotency index of a group algebra

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.