A note on modular group algebras with upper Lie nilpotency indices

Abstract

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