Finite primitive groups and edge-transitive hypergraphs

TL;DR

This paper classifies all finite primitive groups that can serve as automorphism groups of edge-transitive hypergraphs, addressing a problem posed by Babai and Cameron.

Contribution

It provides a complete classification of finite primitive groups acting as automorphism groups of edge-transitive hypergraphs, solving a longstanding open problem.

Findings

Identified all finite primitive groups as automorphism groups of edge-transitive hypergraphs

Resolved the problem posed by Babai and Cameron

Established a comprehensive classification in this area

Abstract

We determine all finite primitive groups that are automorphism groups of edge-transitive hypergraphs. This gives an answer to a problem proposed by Babai and Cameron