Abstract

Height and relational complexity are two numerical invariants that can be associated with any finite permutation group. The relational complexity of a finite permutation group was introduced by Cherlin in 1996. Very little is known about relational complexity in many specific cases and it can be rather difficult to compute it for any given permutation group.

The height of a finite permutation group on a set Ω is defined as the maximum size of an independent set, where a subset of Ω of is said to be independent if its pointwise stabilizer is not equal to the pointwise stabilizer of a proper subset. It turns out that there exists a very useful connection between the height and the relational complexity of a finite permutation group. In particular, the relational complexity is bounded in terms of the height of the group.

In this talk we will introduce these invariants and we will see how they are connected. Moreover, we will provide a computation of the height of all almost simple primitive groups with socle PSL2 in their natural action on projective 1-space and this will give us some information about the relational complexity of this action.