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

#### 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11587/331129
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