Abelian Carter subgroups in finite permutation groups

TL;DR

This paper proves that finite permutation groups with a regular abelian self-normalizing subgroup are necessarily soluble, advancing understanding of their structural properties.

Contribution

It establishes a new criterion linking the existence of a regular abelian self-normalizing subgroup to the solubility of finite permutation groups.

Findings

Finite permutation groups with such subgroups are soluble

Provides a structural characterization of these groups

Enhances classification of permutation groups based on subgroup properties

Abstract

We show that a finite permutation group containing a regular abelian self-normalizing subgroup is soluble.