Ulla Karhumäki - Primitive pseudofinite permutation groups of finite SU-rank

jeudi 27 nov. 2025, 15:00 → 16:00 Europe/Paris

112 (ICJ)

A (definably) primitive permutation group (G,X) is a group G together with a faithful action on a set X such that there are no proper nontrivial (definable) G-invariant equivalence relations on X. A rough classification of primitive permutation groups of finite Morley rank was proven by Macpherson and Pillay and, using that, Borovik and Cherlin showed that if (G,X) is a definably primitive permutation group of finite Morley rank, then RM(G) can be bounded in terms of RM(X). We show an analogue of this result in pseudofinite finite SU-rank context. Namely, using classification results by Liebeck, Macpherson and Tent, we show that if (G,X) is a pseudofinite definably primitive permutation group of finite SU-rank then SU(G) can be bounded as a function of SU(X). This is joint work with Nick Ramsey.