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

2015/07/03 by Cai-Heng Li, Cheryl E. Praeger, Li, Cai-Heng +3
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.1507.01049

arxiv created 2015/07/03 · arxiv updated 2015/07/07

Abstract

We study (G,2)-arc-transitive graphs for innately transitive permutation groups G such that G can be embedded into a wreath product \symΓ\wr\syℓ acting in product action on Γ^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 120² vertices whose automorphism group is \aut\sp 44. We prove that under certain conditions no more such graphs exist.

Related

• Three types of inclusions of innately transitive permutation groups into wreath products in product action
• Locally s-arc-transitive graphs arising from product action
• Innately transitive subgroups of wreath products in product action
• Three local actions in 6-valent arc-transitive graphs
• On 2-arc-transitive graphs of product action type