AI 中文总结
研究基座为\(E_7(q)\)或\(E_8(q)\)的几乎单群在\(s\)-弧传递有向图上的本原作用，结合前人工作，回答了关于有限连通\(G\)-顶点本原\(s\)-弧传递有向图（非有向圈）中\(s\)是否有上界的问题。
AI 中文摘要
本文研究了基座为\(E_7(q)\)或\(E_8(q)\)的几乎单群在\(s\)-弧传递有向图上的本原作用。研究动机可追溯到关于有限连通\(G\)-顶点本原\(s\)-弧传递有向图（非有向圈）中\(s\)是否有上界的问题。Giudici和Xia已将该问题简化到\(G\)几乎单的情形。本文延续之前对\({}^3\!D_4(q)\)等群的研究，结合他人对\({}^2\!B_2(q)\)和\({}^2\!G_2(q)\)的工作，回答了所有例外群的该问题。
英文摘要
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.
