Title: Pseudo-finite groups containing an involution with a finite centralizer.

Abstract: An infinite group is said to be pseudo-finite if it is elementarily equivalent to a non-principal ultraproduct of finite groups. Thus, roughly speaking, a pseudo-finite group is a suitable model-theoretic limit of an infinite family of finite groups. The purpose of this talk is to explain how using pseudo-finite groups one can give an alternative proof of the following result of Hartley and Meixner: A finite group G containing an involution x with a centralizer of size n has a normal subgroup H of n-bounded index whose derived subgroup H' is centralized by x. This is joint work with Nadja Hempel.

Abstract: An infinite group is said to be pseudo-finite if it is elementarily equivalent to a non-principal ultraproduct of finite groups. Thus, roughly speaking, a pseudo-finite group is a suitable model-theoretic limit of an infinite family of finite groups. The purpose of this talk is to explain how using pseudo-finite groups one can give an alternative proof of the following result of Hartley and Meixner: A finite group G containing an involution x with a centralizer of size n has a normal subgroup H of n-bounded index whose derived subgroup H' is centralized by x. This is joint work with Nadja Hempel.

## Date:

Thu, 23/03/2017 - 12:00 to 13:00

## Location:

Manchester 209