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

TL;DR

This paper characterizes finite groups acting arc-transitively on maps with square-free Euler characteristic, classifying groups based on their Sylow subgroups, and presents associated infinite families of regular maps.

Contribution

It completes the classification of finite groups acting on such maps and introduces new infinite families of regular maps with square-free Euler characteristic.

Findings

Finite groups with specific Sylow subgroup structures are classified.

Infinite families of regular maps with square-free Euler characteristic are presented.

A comprehensive characterization of group actions on these maps is achieved.

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.