Logic Seminar
Nick Ramsey (Notre Dame)
Title: A Borovik-Cherlin bound for primitive pseudo-finite permutation groups
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.