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

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• 作者：Cai-Heng Li^a ; ^{cai.heng.li@uwa.edu.au" class="auth_mail" title="E-mail the corresponding author} ; ; Cheryl E. Praeger^a ; ^{cheryl.praeger@uwa.edu.au" class="auth_mail" title="E-mail the corresponding author} ; ; Csaba Schneider^b ; ^{csaba@mat.ufmg.br" class="auth_mail" title="E-mail the corresponding author} ;
• 关键词：20B05 ; 20B35 ; 20B25
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：220
• 期：7
• 页码：2683-2700
• 全文大小：534 K

文摘

We study (G,2)$(G,2)$-arc-transitive graphs for innately transitive permutation groups G such that G   can be embedded into a wreath product $\mathsf{Sym}\mathrm{\Gamma }\mathsf{wr}{\mathsf{S}}_{\ell }$ acting in product action on Γ^ℓ${\mathrm{\Gamma }}^{\ell }$. We find two such connected graphs: the first is Sylvester's double six graph with 36 vertices, while the second is a graph with 120² vertices whose automorphism group is $\mathsf{Aut}\mathsf{Sp}(4,4)$. We prove that under certain conditions no more such graphs exist.