Zoom Link: https://huji.zoom.us/j/87810512383?pwd=EJ1tjEuOzGuqbZzhzN7nQs5sUb7aRY.1
Title: Supersimple pseudofinite primitive permutation groups of finite SU-rank
Abstract: A (definably) primitive permutation group (G,X) is a group G together with a transitive faithful and definable action on X such that there are no proper nontrivial (definable) G-invariant equivalence relations on X. Definably primitive permutation groups of finite Morley rank are well-studied: in particular, it is shown by Macpherson and Pillay that such a group with infinite point stabilisers is actually primitive and by Cherlin and Borovik that, given such a group (G,X), the Morley rank of G can be bounded in terms of the Morley rank of X. We show similar results for supersimple pseudofinite definably primitive permutation group (G,X) of finite SU-rank: we first show that (G,X) is primitive if and only if the point stabilisers are infinite. This then allows us to apply classification results by Liebeck, Macpherson and Tent on (G,X) so that we may bound the SU-rank of G in terms of the SU-rank of X. This is joint work in with Nick Ramsey.