TY - JOUR

T1 - Engel-like characterization of radicals in finite dimensional Lie algebras and finite groups

AU - Bandman, Tatiana

AU - Borovoi, Mikhail

AU - Grunewald, Fritz

AU - Kunyavskii, Boris

AU - Plotkin, Eugene

PY - 2006/4

Y1 - 2006/4

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33645533098&partnerID=8YFLogxK

U2 - 10.1007/s00229-006-0627-0

DO - 10.1007/s00229-006-0627-0

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:33645533098

SN - 0025-2611

VL - 119

SP - 465

EP - 481

JO - Manuscripta Mathematica

JF - Manuscripta Mathematica

IS - 4

ER -