Stable pseudofinite groups
Seminar Room 1, Newton Institute
I will discuss recent work with Katrin Tent, in which it is shown that any stable pseudofinite group is soluble-by-finite. The `Mekler Construction' gives stable pseudofinite groups which are not abelian-by-finite. We do not know whether every stable pseudofinite group is nilpotent-by-finite.