Groups and Dynamics Seminar

Date: September 22, 2021

Time: 3:00PM - 4:00PM

Location: online

Speaker: Andrei Rapinchuk, University of Virginia

Title: Groups with bounded generation: old and new

Abstract: A group is said to have bounded generation (BG) if it is a finite product of cyclic subgroups. We will survey the known examples of groups with (BG) and their properties. We will then report on a recent result (joint with P. Corvaja, J. Ren and U. Zannier) that non-virtually abelian anisotropic linear groups (i. e. those consisting entirely of semi-simple elements) are not boundedly generated. The proofs rely on number-theoretic techniques.