Most primitive groups are full automorphism groups of edge-transitive hypergraphs

Abstract

We prove that, for a primitive permutation group G acting on a set of size n, other than the alternating group, the probability that Aut(X,Y^G) = G for a random subset Y of X, tends to 1 as n tends to infinity. So the property of the title holds for all primitive groups except the alternating groups and finitely many others. This answers a question of M. Klin. Moreover, we give an upper bound n^{1/2+ε} for the minimum size of the edges in such a hypergraph. This is essentially best possible.

To appear in special issue of Journal of Algebra in memory of Akos Seress

Cited by in corpus (2)

• Finite primitive groups and edge-transitive hypergraphs
• Most switching classes with primitive automorphism groups contain graphs with trivial groups