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

Tatiana Bandman, Mikhail Borovoi, Fritz Grunewald, Boris Kunyavskii, Eugene Plotkin

Research output: Contribution to journalArticlepeer-review

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 G such that for any x G the nth 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.

Original languageEnglish
Pages (from-to)465-481
Number of pages17
JournalManuscripta Mathematica
Volume119
Issue number4
DOIs
StatePublished - Apr 2006

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