On the structure of vertex stabilizers of arc-transitive locally quasiprimitive graphs

期刊论文
出版模式：

开放获取
发表日期：

2024年6月12日

查看全文

J. van Bon

摘要

Let $\Delta $ $Δ$ be a connected arc-transitive G-graph which is locally finite and locally quasiprimitive. Let $\{x,y\}$ ${x, y}$ be an edge of $\Delta $ $Δ$ . A relation between $G_x^{[1]}/O_p(G_x^{[1]})$ $G_{x}^{[1]} / O_{p} (G_{x}^{[1]})$ and the existence of certain normal subgroups of $G_x^{\Delta (x)}$ $G_{x}^{Δ (x)}$ and $G_{x,y}^{\Delta (x)}$ $G_{x, y}^{Δ (x)}$ is established. This is then used to determine the vertex stabilizers of a class of 2-arc-transitive graphs with trivial edge kernel.