Exceptional groups and the s-arc-transitivity of vertex-primitive digraphs, II

Lei Chen; Fu-Gang Yin

Exceptional groups and the s-arc-transitivity of vertex-primitive digraphs, II

Group Theory 2026-07-16 v1

Authors: Lei Chen , Fu-Gang Yin

Abstract

In this paper, we study the primitive actions of almost simple groups with socle $E_7(q)$ or $E_8(q)$ on an $s$ -arc-transitive digraph. Our motivation goes back to the question of whether $s$ is bounded above for finite connected $G$ -vertex-primitive $s$ -arc-transitive digraphs that are not directed cycles. The question has been reduced by Giudici and Xia to the case where $G$ is almost simple. This work succeeds our 2025 paper (Yin and Chen), which addressed ${}^3\!D_4(q)$ , $G_2(q)$ , ${}^2\!F_4(q)'$ , $F_4(q)$ , $E_6(q)$ , and ${}^2\!E_6(q)$ . Together with Chen, Giudici, and Praeger's work on ${}^2\!B_2(q)$ and ${}^2\!G_2(q)$ , it answers the question for all exceptional groups.

Keywords

exceptional groups s-arc-transitive digraphs vertex-primitive almost simple groups E7(q) E8(q)

Cite

@article{arxiv.2607.14603,
  title  = {Exceptional groups and the s-arc-transitivity of vertex-primitive digraphs, II},
  author = {Lei Chen and Fu-Gang Yin},
  journal= {arXiv preprint arXiv:2607.14603},
  year   = {2026}
}