Let $KG$ be a non-commutative Lie solvable group algebra of a group $G$ over a field $K$ of positive characteristic $p$. A. Shalev [\emph{The derived length of Lie soluble group rings I}, J. Pure and Appl. Algebra {\bf{78}} (1992), 291-300] proved that $dl_L(KG)\geq \lceil \log_{2}(p+1)\rceil $ 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.
Group algebras with minimal Lie derived length
SPINELLI, Ernesto
2008-01-01
Abstract
Let $KG$ be a non-commutative Lie solvable group algebra of a group $G$ over a field $K$ of positive characteristic $p$. A. Shalev [\emph{The derived length of Lie soluble group rings I}, J. Pure and Appl. Algebra {\bf{78}} (1992), 291-300] proved that $dl_L(KG)\geq \lceil \log_{2}(p+1)\rceil $ 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.File in questo prodotto:
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