On -arc transitive hypergraphs

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