On the Lie nilpotency index of modular group algebras

TL;DR

This paper classifies modular group algebras with a specific upper Lie nilpotency index of 10p-8, extending previous classifications up to 9p-7, and explores the conditions under which these algebras are Lie nilpotent.

Contribution

It provides a new classification of modular group algebras with upper Lie nilpotency index 10p-8, advancing understanding of their structure in the context of Lie nilpotency.

Findings

Classified modular group algebras with upper Lie nilpotency index 10p-8

Extended previous classifications up to 9p-7

Identified conditions for Lie nilpotency in these algebras

Abstract

Let $KG$ be the modular group algebra of an arbitrary group $G$ over a field $K$ of characteristic $p>0$. It is seen that if $KG$ is Lie nilpotent, then its lower as well as upper Lie nilpotency index is at least $p+1$. The classification of group algebras $KG$ with upper Lie nilpotency index $t^{L}(KG)$ upto $9p-7$ have already been determined. In this paper, we classify the modular group algebra $KG$ for which the upper Lie nilpotency index is $10p-8$.