Group algebras with minimal Lie derived length

摘要

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 dl(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. (C) 2008 Elsevier Inc. All rights reserved.