Sharply doubly transitive groups with saturation conditions

TL;DR

This paper investigates specific conditions under which sharply doubly transitive groups possess an abelian normal divider, contributing to the understanding of their structural properties.

Contribution

It introduces new saturation conditions that guarantee the existence of an abelian normal divider in sharply doubly transitive groups.

Findings

Identification of conditions leading to abelian normal dividers

Extension of known results on sharply doubly transitive groups

Structural insights into permutation group properties

Abstract

A number of conditions were found under which a sharply doubly transitive permutation group has an abelian normal divider.