On the Lie nilpotency indices of modular group algebras

Abstract

Let KG be the group algebra of a group G over a field K of characteristic \(p>0\). The classification of group algebras KG for which Lie nilpotency indices are maximal or almost maximal has already been determined. After that Bovdi and Srivastava classified Lie nilpotent group algebras with \(t^{L}(KG)=|G^{\prime }| - 2p +3,|G^{\prime }| - 3p +4\) and \( |G^{\prime }| - 4p +5.\) In this paper, our aim is to classify the group algebras KG for which \(t^{L}(KG)=|G^{\prime }| - 5p +6,|G^{\prime }| - 6p +7\) and \( |G^{\prime }| - 7p +8.\)