Group algebras with minimal Lie derived length

Abstract

Let KG be a non-commutative Lie solvable group algebra of a group G over a field K of positive characteristic p. In [A. Shalev, The derived length of Lie soluble group rings I, J. Pure Appl. Algebra 78 (1992) 291–300] Shalev proved that d l L ( KG ) ⩾ ⌈ log 2 ( p + 1 ) ⌉ and posed the question of characterizing group algebras for which this lower bound is achieved. In this note the solution to this question is given.