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arXiv 1710.01166math.CO
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允许点传递非交换单群的具有可解稳定器的七叶对称图

Heptavalent symmetric graphs with solvable stabilizers admitting vertex-transitive non-abelian simple groups

Jia-Li Du, Yan-Quan Feng, Yu-Qin Liu

备注：
9. arXiv admin note: substantial text overlap with arXiv:1701.01187
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摘要：

一个图$Γ$称为对称图，如果它的自同构群$\rm Aut(Γ)$传递地作用在$Γ$的弧集上.本文证明了：如果$Γ$是一个有可解稳定子的有限连通七价对称图，且允许一个自同构的点传递非阿贝尔单群$G$，则要么$G$在$Γ$中正规，要么$\rm Aut(Γ)$包含一个非阿贝尔单群正规子群$T$，使得$G\leq T$和$(G,T)$是非阿贝尔单群的$11$可能例外对之一.此外，如果$G$在$Γ$的顶点集上是正则的，则例外对$(G,T)$是$7$可能对之一，并且如果$G$是弧传递的，则例外对$(G,T)=(A_{17},A_{18})$或$(A_{35},A_{36})$。

英文摘要：

A graph $Γ$ is said to be symmetric if its automorphism group $\rm Aut(Γ)$ acts transitively on the arc set of $Γ$. In this paper, we show that if $Γ$ is a finite connected heptavalent symmetric graph with solvable stabilizer admitting a vertex-transitive non-abelian simple group $G$ of automorphisms, then either $G$ is normal in $\rm Aut(Γ)$, or $\rm Aut(Γ)$ contains a non-abelian simple normal subgroup $T$ such that $G\leq T$ and $(G,T)$ is explicitly given as one of $11$ possible exception pairs of non-abelian simple groups. Furthermore, if $G$ is regular on the vertex set of $Γ$ then the exception pair $(G,T)$ is one of $7$ possible pairs, and if $G$ is arc-transitive then the exception pair $(G,T)=(A_{17},A_{18})$ or $(A_{35},A_{36})$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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