Engel-like characterization of radicals in finite dimensional Lie algebras and finite groups

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dc.creatorBandman, Tatiana
dc.creatorBorovoi, Mikhail
dc.creatorGrunewald, Fritz
dc.creatorKunyavskii, Boris
dc.creatorPlotkin, Eugene
dc.date2004-11-21
dc.date.accessioned2026-07-07T08:52:12Z
dc.date.available2026-07-07T08:52:12Z
dc.descriptionA 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.
dc.description17 pages
dc.identifierhttps://arxiv.org/abs/math/0411463
dc.identifierhttp://arxiv.org/abs/math/0411463
dc.identifierManuscripta Math. 119 (2006), 365-381
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/145202
dc.subjectGroup Theory
dc.subjectRings and Algebras
dc.subject20D25; 17B05; 17B01
dc.titleEngel-like characterization of radicals in finite dimensional Lie algebras and finite groups
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