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.