Finite groups and arc-transitive maps of square-free Euler characteristic

2025/11/18 by Peice Hua, Hua, P. C., Cai Heng Li +5
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2511.14818

openalex publication_date 2025/11/18 · openalex created_date 2025/11/23 · openalex updated_date 2026/07/31

Abstract

A characterization is completed for finite groups acting arc-transitively on maps with square-free Euler characteristic, associated with infinite families of regular maps of square-free Euler characteristic presented. This is based on a classification of finite groups of which each Sylow subgroup has a cyclic or dihedral subgroup of prime index.

Citations

• A classification of vertex-reversing maps with Euler characteristic coprime to the edge number
• Finite 2-groups having a cyclic or dihedral maximal subgroup and arc-transitive maps
• Locally Finite Vertex-Rotary Maps and Coset Graphs with Finite Valency and Finite Edge Multiplicity

Cited by

• Finite 2-groups having a cyclic or dihedral maximal subgroup and arc-transitive maps

Related

• Finite 2-groups having a cyclic or dihedral maximal subgroup and arc-transitive maps
• Arc-transitive maps with edge number coprime to the Euler characteristic -- I
• Arc-transitive maps with coprime Euler characteristic and edge number -- II
• A classification of vertex-reversing maps with Euler characteristic coprime to the edge number
• Finite simple automorphism groups of edge-transitive maps