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arXiv · 1710.09518

Vertex-primitive $s$-arc-transitive digraphs of linear groups

Michael Giudici·Cai Heng Li·Binzhou Xia
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Abstract

We study $G$-vertex-primitive and $(G,s)$-arc-transitive digraphs for almost simple groups $G$ with socle $\mathrm{PSL}_n(q)$. It turns out that $s\leqslant2$ for such digraphs, which provides the first step in determining an upper bound on $s$ for all the vertex-primitive $s$-arc-transitive digraphs.

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Michael Giudici, Cai Heng Li, Binzhou Xia. 2019-04-17. Vertex-primitive $s$-arc-transitive digraphs of linear groups. https://arxiv.org/abs/1710.09518

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