Lie nilpotency Index of a modular group algebra

TL;DR

This paper classifies modular group algebras with specific upper Lie nilpotency indices for certain values of k, extending previous classifications for smaller k.

Contribution

It provides a classification of modular group algebras with upper Lie nilpotency index for k=14 and 15, filling gaps in existing characterizations.

Findings

Classified modular group algebras for k=14 and 15.

Extended previous results for k≤13.

Identified conditions for specific Lie nilpotency indices.

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 $t^{L}(KG)= \vert G^{\prime}\vert - k(p-1) + 1$ for $k=14$ and $15$. Group algebras of upper Lie nilpotency index $\vert G^{\prime}\vert - k(p-1) + 1$ for $k\leq 13$, have already been characterized completely.