On the order of arc-stabilisers in arc-transitive graphs with prescribed local group

Abstract

Let $\Gamma$ be a connected $G$-arc-transitive graph, let $uv$ be an arc of $\Gamma$ and let $L$ be the permutation group induced by the action of the vertex-stabiliser $G_v$ on the neighbourhood $\Gamma (v)$. We study the problem of bounding $|G_{uv}|$ in terms of $L$ and the order of $\Gamma$.

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