Dugald Macpherson (Leeds)

Omega-categorical pseudofinite groups

I will discuss recent joint work with Katrin Tent on omega-categorical groups which are pseudofinite, i.e. satisfy every first order  sentence which is true of all finite groups. It is fairly easy to show that they are nilpotent-by-finite, and we conjecture that they are finite-by-abelian-by-finite, and can reduce this to the nilpotent class 2 case. We show that  certain class 2 groups constructed by amalgamation are NOT pseudofinite – in particular there is an example with supersimple theory which is not pseudofinite.