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 class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022404915003485&_mathId=si1.gif&_user=111111111&_pii=S0022404915003485&_rdoc=1&_issn=00224049&md5=8ae2ba56f8f091eb9717a556b84615d3" title="Click to view the MathML source">(G,2)class="mathContainer hidden">class="mathCode">$(G,2)$-arc-transitive graphs for innately transitive permutation groups G such that G   can be embedded into a wreath product class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022404915003485&_mathId=si2.gif&_user=111111111&_pii=S0022404915003485&_rdoc=1&_issn=00224049&md5=15b4a1ef87da8f912cfdce913e60e0c8">class="imgLazyJSB inlineImage" height="16" width="80" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022404915003485-si2.gif">class="mathContainer hidden">class="mathCode">$\mathsf{Sym}\mathrm{\Gamma }\mathsf{wr}{\mathsf{S}}_{\ell }$ acting in product action on class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022404915003485&_mathId=si3.gif&_user=111111111&_pii=S0022404915003485&_rdoc=1&_issn=00224049&md5=f7201d27fb557b6f45377454a5b4109f" title="Click to view the MathML source">Γ^ℓclass="mathContainer hidden">class="mathCode">${\mathrm{\Gamma }}^{\ell }$. 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 class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022404915003485&_mathId=si4.gif&_user=111111111&_pii=S0022404915003485&_rdoc=1&_issn=00224049&md5=904b834491ed6f3d392582257275fd8a">class="imgLazyJSB inlineImage" height="16" width="81" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022404915003485-si4.gif">class="mathContainer hidden">class="mathCode">$\mathsf{Aut}\mathsf{Sp}(4,4)$. We prove that under certain conditions no more such graphs exist.