Finite simple automorphism groups of edge-transitive maps

TL;DR

This paper classifies non-abelian finite simple groups that serve as automorphism groups of edge-transitive maps across all 14 Graver-Watkins classes, extending previous classifications for regular and chiral maps.

Contribution

It provides a comprehensive classification of simple automorphism groups for edge-transitive maps, covering all Graver-Watkins classes, building on earlier work for regular and chiral maps.

Findings

Identifies all non-abelian finite simple groups as automorphism groups in each class.

Extends classification results to all 14 Graver-Watkins classes.

Builds on prior classifications for regular and chiral maps.

Abstract

Building on earlier results for regular maps and for orientably regular chiral maps, we classify the non-abelian finite simple groups arising as automorphism groups of maps in each of the 14 Graver-Watkins classes of edge-transitive maps.