Lie nilpotency Index of a modular group algebra

Abstract

In this paper, we classify the modular group algebra $KG$ of a group $G$ over a field $K$ of characteristic $p>0$ having upper Lie nilpotency index $t^L(KG)=|G^{\prime }|-k(p-1)+1$ for $k=14$ and $15$. Group algebras of upper Lie nilpotency index $|G^{\prime }|-k(p-1)+1$ for $k\le 13$, have already been characterized completely.