Black box groups and groups of finite Morley rank
Seminar Room 1, Newton Institute
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.