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24 April 2024

» arxiv » math.GR/0411463

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Engel-like characterization of radicals in finite dimensional Lie algebras and finite groups
Tatiana Bandman ; Mikhail Borovoi ; Fritz Grunewald ; Boris Kunyavskii ; Eugene Plotkin ;
Date:	21 Nov 2004
Subject:	Group Theory; Rings and Algebras MSC-class: 20D25; 17B05; 17B01 \| math.GR math.RA
Abstract:	A classical theorem of R. Baer describes the nilpotent radical of a finite group G as the set of all Engel elements, i.e. elements y in G such that for any x in G the n-th commutator [x,y,...,y] equals 1 for n big enough. We obtain a characterization of the solvable radical of a finite dimensional Lie algebra defined over a field of characteristic zero in similar terms. We suggest a conjectural description of the solvable radical of a finite group as the set of Engel-like elements and reduce this conjecture to the case of a finite simple group.
Source:	arXiv, math.GR/0411463
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