On the order of vertex-stabilisers in vertex-transitive graphs with local group or

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• 作者：Pablo Spiga^a ; ^{pablo.spiga@unimib.it" class="auth_mail" title="E-mail the corresponding author} ; Gabriel Verret^b ; ^c ; ¹ ; ^{gabriel.verret@uwa.edu.au" class="auth_mail" title="E-mail the corresponding author}
• 关键词：05E18 ; 20B25
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：15 February 2016
• 年：2016
• 卷：448
• 期：Complete
• 页码：174-209
• 全文大小：700 K

文摘

Let p   be a prime and let L$\mathcal{L}$ be either the intransitive permutation group C_p×C_p${\mathrm{C}}_p\times {\mathrm{C}}_p$ of degree 2p   or the transitive permutation group ${\mathrm{C}}_p\mathrm{wr}{\mathrm{C}}_2$ of degree 2p. Let Γ be a connected G-vertex-transitive and G-edge-transitive graph and let v   be a vertex of Γ. We show that if the permutation group induced by the vertex-stabiliser G_v$G_v$ on the neighbourhood Γ(v)$\mathrm{\Gamma }(v)$ is isomorphic to L$\mathcal{L}$ then either |V(Γ)|≥p|G_v|log_p⁡(|G_v|/2)$|\mathrm{V}(\mathrm{\Gamma })|\ge p|G_v|{\log }_p(|G_v|/2)$, or |V(Γ)|$|\mathrm{V}(\mathrm{\Gamma })|$ is bounded by a constant depending only on p, or Γ is a very-well understood graph. This generalises a few recent results.