Colloquium
3:00 p.m., Friday (April 15, 2005)
West Mall Annex 110 (PIMS Facility)
Boris Kunyavskii
Bar Ilan University
Characterization of radicals in finite dimensional Lie algebras and finite groups
Abstract: Classical theorems of Engel and Zorn describe the classes
of finite dimensional nilpotent Lie algebras and finite
groups in terms of twovariable identities. Recently similar
characterizations have been obtained for the classes of finite
dimensional solvable Lie algebras and finite solvable groups
(the proof of the latter one required a good bunch of arithmetic
geometry and computer algebra).
More generally, a theorem of Baer describes the nilpotent radical
of a finite group in terms of Engel elements. Our goal is to
obtain similar characterizations for the solvable radical of
a finite dimensional Lie algebra and of a finite group.
This talk is based on several (finished as well as ongoing)
projects joint with T. Bandman, M. Borovoi, N. Gordeev, G.M. Greuel,
F. Grunewald, D. Nikolova, G. Pfister, E. Plotkin, and A. Shalev.
Refreshments will be served at 2:45 p.m. in the PIMS 1st floor lounge.
