Let $\Delta$ be a connected arc-transitive $G$-graph which is locally finite and locally quasiprimitive. Let $\{x,y\}$ be an edge of $\Delta$. A relation between $G_x^{[1]}/O_p(G_x^{[1]})$ and the existence of certain normal subgroups of $G_x^{\Delta (x)}$ and $G_{x,y}^{\Delta (x)}$ is established. This is then used to determine the vertex stabilizers of a class of 2-arc transitive graphs with trivial edge kernel.
On the structure of vertex stabilizers of arc-transitive locally quasiprimitive graphs
van Bon J.
2024-01-01
Abstract
Let $\Delta$ be a connected arc-transitive $G$-graph which is locally finite and locally quasiprimitive. Let $\{x,y\}$ be an edge of $\Delta$. A relation between $G_x^{[1]}/O_p(G_x^{[1]})$ and the existence of certain normal subgroups of $G_x^{\Delta (x)}$ and $G_{x,y}^{\Delta (x)}$ is established. This is then used to determine the vertex stabilizers of a class of 2-arc transitive graphs with trivial edge kernel.File in questo prodotto:
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