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

Michael Giudici; Cai Heng Li; Binzhou Xia

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

Combinatorics 2019-04-18 v3

Authors: Michael Giudici , Cai Heng Li , Binzhou Xia

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.

Keywords

permutation groups

Cite

@article{arxiv.1710.09518,
  title  = {Vertex-primitive $s$-arc-transitive digraphs of linear groups},
  author = {Michael Giudici and Cai Heng Li and Binzhou Xia},
  journal= {arXiv preprint arXiv:1710.09518},
  year   = {2019}
}

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