Infinite simple characteristic quotientsGeometric Group Theory Oberseminar

by Francesco Fournier-Facio (Cambridge)

Wednesday Jan 8, 2025, 11:00 AM → 12:00 PM Europe/Berlin

Endenicher Allee 60/0-003 - Seminarraum (Mathezentrum)

A topic that received a lot of attention 50 years ago is that of the rank of finitely generated groups, i.e. the minimal size of a generating set. A research programme initiated by James Wiegold aims at understanding the rank of finitely generated groups, and how this relates to the rank of their direct powers. In this context, he asked about the existence of infinite simple characteristic quotients of free groups.

I will review this framework, introduce several open questions – old and new – and present a solution to Wiegold’s problem.

Joint with Rémi Coulon.