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.
Group algebras with minimal Lie derived length / Spinelli, Ernesto. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - STAMPA. - 320:5(2008), pp. 1908-1913. [10.1016/j.jalgebra.2007.05.029]
Group algebras with minimal Lie derived length
SPINELLI, ERNESTO
2008
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 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
