On ss-arc transitive hypergraphs

A hypergraph is ss-arc transitive if its automorphism group acts transitively on the set of its ss-arcs. In this paper, we study ss-arc transitive hypergraphs. We show that if a hypergraph has degree at least three and all edges of sizes at least three, then s≤5s≤5. Besides, given an ss-arc transitive hypergraph, we prove that there are infinitely many ss-arc transitive hypergraphs that cover the given one. These results extend to hypergraph classical results by Tutte, Weiss and Biggs for graphs.