Quasiprimitive groups containing a transitive alternating group

TL;DR

This paper classifies quasiprimitive permutation groups that contain a transitive subgroup isomorphic to an alternating group, expanding understanding of their structure and properties.

Contribution

It provides a complete classification of quasiprimitive groups with a transitive alternating subgroup, a new result in permutation group theory.

Findings

Classification of such quasiprimitive groups achieved

Identification of structural properties of these groups

Extension of known results in permutation group classification

Abstract

This paper classifies quasiprimitive permutation groups with a transitive subgroup which is isomorphic to $\A_n$ for some $n\geqslant5$.