2025/07/21 by Xu, Songnian, Wong, Dein, Zhang, Chi +1 · 1 citation
#05C20 #05C25 #FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2507.15405
Let G be a group and m a positive integer. We say an m-Cayley digraph Γ over G is a digraph that admits a group of automorphisms isomorphic to G acting semiregularly on the vertex set with m orbits. The digraph Σ is k-regular if there exists a non-negative integer k such that every vertex has out-valency and in-valency equal to k. All digraphs considered in this paper are regular. We say that G admits an oriented m-semiregular representation (abbreviated as OmSR) if there exists a regular m-Cayley digraph Γ over G such that Γ is oriented and its automorphism group is isomorphic to G. In particular, an O1SR is called an ORR. Xia et al. \citex2 provided a classification of finite simple groups admitting an ORR of valency 2. Furthermore, in 2022, Du et al. \citedu2 proved that most finite simple groups admit an OmSR of valency 2 for m ≥ 2, except for a few exceptional cases. In this paper, we classify the finite groups generated by at most two elements that admit an OmSR of valency 3 for m ≥ 2.