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

Cai-Heng Li; Cheryl E. Praeger; Csaba Schneider

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arXiv · 1507.01049

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

Cai-Heng Li·Cheryl E. Praeger·Csaba Schneider

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Abstract

We study $(G,2)$-arc-transitive graphs for innately transitive permutation groups $G$ such that $G$ can be embedded into a wreath product $\sym\Gamma\wr\sy\ell$ acting in product action on $\Gamma^\ell$. 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 $\aut\sp 44$. We prove that under certain conditions no more such graphs exist.

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Cai-Heng Li, Cheryl E. Praeger, Csaba Schneider. 2015-07-03. Inclusions of innately transitive groups into wreath products in product action with applications to $2$-arc-transitive graphs. https://arxiv.org/abs/1507.01049

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