3:00 p.m., Friday (April 15, 2005)
West Mall Annex 110 (PIMS Facility)
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 two-variable 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.