论文标题
弧线传递的cayley图表上具有黄金价值的非亚伯简单群体
Arc-transitive Cayley graphs on nonabelian simple groups with prime valency
论文作者
论文摘要
在2011年，Fang等人。在（J. Combin。理论A 118（2011）1039-1051）提出了以下问题：对有限简单的价值$ d $的非正常原始原始的cayley图进行分类，其中$ d \ leq 20 $或$ d $是质量数字。唯一知道该问题的解决方案的唯一情况是$ d = 3 $。除此之外，考虑了以下问题，已经做出了许多努力来攻击此问题：表征有限的非亚伯简单组，这些群体接受了某些价值$ d \ geq4 $的非正常原始cayley图。即使对于这个问题，也只能在$ d \ leq 5 $或$ d = 7 $的情况下解决，并且顶点稳定器是可解决的。在本文中，我们通过完全解决$ d \ geq 11 $是素数并且可以解决顶点稳定器的情况下解决第二个问题，从而在上述问题方面取得了至关重要的进步。
In 2011, Fang et al. in (J. Combin. Theory A 118 (2011) 1039-1051) posed the following problem: Classify non-normal locally primitive Cayley graphs of finite simple groups of valency $d$, where either $d\leq 20$ or $d$ is a prime number. The only case for which the complete solution of this problem is known is of $d=3$. Except this, a lot of efforts have been made to attack this problem by considering the following problem: Characterize finite nonabelian simple groups which admit non-normal locally primitive Cayley graphs of certain valency $d\geq4$. Even for this problem, it was only solved for the cases when either $d\leq 5$ or $d=7$ and the vertex stabilizer is solvable. In this paper, we make crucial progress towards the above problems by completely solving the second problem for the case when $d\geq 11$ is a prime and the vertex stabilizer is solvable.
