On the lower Lie nilpotency index of a group algebra

Abstract

In this article, we show that if KG is a Lie nilpotent group algebra of a group G over a field K of characteristic p > 0, then t^L (KG) = k if and only if t^L (KG) = k, for k ∈ {5p − 3, 6p − 4}, where t_L (KG) and t^L (KG) are the lower and the upper Lie nilpotency indices of KG, respectively.