Bianca Loda

On the relational complexity for finite primitive groups

About 20 years ago, motivated by questions in model theory, Cherlin introduced the notion of the relational complexity of a permutation group. This is a positive integer which, roughly speaking, gives an indication of how easily the group G can act homogeneously on a relational structure. The main result about this invariant is a conjecture by Cherlin which concerns primitive permutation groups with relational complexity equal to 2. In this talk, we will discuss some progress towards a classification of the primitive permutation groups with “large” relational complexity, with particular interest to primitive groups.