Finite quasiprimitive permutation groups with a metacyclic transitive subgroup

TL;DR

This paper classifies finite quasiprimitive permutation groups containing a metacyclic transitive subgroup, addressing a problem from 1949, and also classifies factorizations of almost simple groups with a metacyclic factor.

Contribution

It provides a complete classification of such groups and factorizations, advancing the understanding of permutation group structures.

Findings

Classification of finite quasiprimitive groups with metacyclic transitive subgroups

Classification of factorizations of almost simple groups with metacyclic factors

Solves a long-standing problem initiated by Wielandt in 1949

Abstract

In this paper, we classify finite quasiprimitive permutation groups with a metacyclic transitive subgroup, solving a problem initiated by Wielandt in 1949. It also involves the classification of factorizations of almost simple groups with a metacyclic factor.