Two-arc-transitive graphs of odd order -- II

TL;DR

This paper classifies 2-arc-transitive graphs of odd order that admit an alternating or symmetric group, showing that subgroups of odd index in large alternating groups have only alternating insoluble composition factors.

Contribution

It provides a classification of 2-arc-transitive graphs of odd order with specific group actions, advancing the understanding of their structure and symmetry properties.

Findings

Subgroups of odd index in large alternating groups have only alternating insoluble composition factors.

A classification of 2-arc-transitive graphs of odd order with alternating or symmetric group actions.

Progress towards a complete classification of 2-arc-transitive graphs of odd order.

Abstract

It is shown that each subgroup of odd index in an alternating group of degree at least 10 has all insoluble composition factors to be alternating. A classification is then given of 2-arc-transitive graphs of odd order admitting an alternating group or a symmetric group. This is the second of a series of papers aiming towards a classification of 2-arc-transitive graphs of odd order.