An Isaac Newton Institute Programme

Model Theory and Applications to Algebra and Analysis

Black box groups and groups of finite Morley rank

2nd March 2004

Author: Alexandre Borovik (The University of Manchester)

Abstract

I will discuss some strange analogies between some probabilistic methods for recognition of "black box" finite groups and the theory of groups of finite Morley rank. As an application and illustration, I will give a short elementary proof of the following fact.

Let G be a group of finite Morley rank. If a Sylow 2-subgroup S of G is cyclic then S intersects trivially with the connected component of G.