Inclusions of innately transitive groups into wreath products in product action with applications to 2-arc-transitive graphs

摘要

We study (G, 2)-arc-transitive graphs for innately transitive permutation groups G such that G can be embedded into a wreath product Sym Gamma wr S-l acting in product action on Gamma(l). We find two such connected graphs: the first is Sylvester's double six graph with 36 vertices, while the second is a graph with 120(2) vertices whose automorphism group is Aut Sp(4,4). We prove that under certain conditions no more such graphs exist. (c) 2016 Elsevier B.V. All rights reserved.