On the Lie nilpotency index of modular group 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.