学 术 报 告
报告题目: On valency problems of the Saxl graphs
报告摘要: Let $G$ be a permutation group on a set $\Omega$ and recall that a base for $G$ is a subset of $\Omega$ such that its pointwise stabiliser is trivial. In a recent paper, Burness and Giudici introduced the Saxl graph of $G$, denoted $\Sigma(G)$, with vertex set $\Omega$ and two vertices adjacent if they form a base. If $G$ is transitive, then $\Sigma(G)$ is vertex-transitive and it is natural to consider its valency (which we refer to as the valency of $G$). In this talk I will show a general method for computing the valency of any finite transitive group. As an application, we calculate the valency of every almost simple primitive group with an alternating socle and soluble stabiliser which extend the results of Burness and Giudici on almost simple primitive groups with prime-power or odd valency. This is a joint work with Hong Yi Huang.