Abstract : A primitive permutation group $(X, G)$ is a group $G$ together with an action of $G$ on $X$ such that there are no nontrivial equivalence relations on $X$ preserved by $G$. An rough classification of primitive permutation groups of finite Morley rank, modeled on the O'Nan-Scott theorem for finite primitive permutation groups, has been carried out by Macpherson and Pillay and this classification was then used by Borovik and Cherlin to prove that if $(X, G)$ is a primitive permutation group of finite Morley rank, the rank of $G$ can be bounded in terms of the rank of $X$. We study the analogous situation for pseudo-finite primitive permutation groups of finite SU-rank, building both on supersimple group theory and classification results of Liebeck-Macpherson-Tent. This is joint work in progress with Ulla Karhumäki.

Keywords : Permutation groups; simplicity theory