Antonio Montero: On the order of uniprimitivity permutation groups

A classical well-known result by Babai claims that any a primitive permutation group containing a cycle of prime length fixing at least three points must contain the alternating group. While exploring related results we came across with one paper (also by Babai) that proves deep group theoretical results using purely combinatorial techniques. In the talk we shall review some of these techniques and present some of the results.