Highly arc transitive digraphs (Q1123206)

A digraph is said to be (G,s) transitive if G acts as a group of automorphisms which is transitive on length s edge sequences. The author constructs examples \(C_ r(v,s)\) with vertex set \(Z_ r\times Z^ s_ v\) with automorphism group \(S_ v\) wr \(Z_ r\) and shows it is (G,s) arc transitive but not \((G,s+1)\) arc transitive for any s. She gives structure theorems involving normal subgroups and also in the case G acts primitively on the vertices.