Lie nilpotency indices of modular group algebras II

Abstract

Let [Formula: see text] be the modular group algebra of a group [Formula: see text] over a field [Formula: see text] of characteristic [Formula: see text]. The classification of the group algebras [Formula: see text] with upper Lie nilpotency index [Formula: see text] greater than or equal to [Formula: see text] has already been done. In this paper, we determine the group algebras [Formula: see text] such that [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] or [Formula: see text].

A note on the upper Lie nilpotency index of a group algebra

“…A complete description of Lie nilpotent modular group algebras KG of upper Lie nilpotency index t L (KG) ≤ 9p − 7 is given in [9,10,11,12,17]. On the other hand, group algebras with t L (KG) = |G ′ | − k(p − 1) + 1 for k ≤ 13 are classified in [2,3,5,6,13,14,18]. In this paper, we classify the group algebra KG with t L (KG) = |G ′ | − k(p − 1) + 1 for k = 14 and 15. our terminology and notations are same as in [10].…”