Sharply $2$-transitive groups

TL;DR

This paper presents a new explicit construction of sharply 2-transitive groups that have fixed point free involutions and lack nontrivial abelian normal subgroups, advancing the understanding of their algebraic structure.

Contribution

It provides the first explicit construction of such sharply 2-transitive groups with these specific properties, filling a gap in the existing mathematical literature.

Findings

Constructed sharply 2-transitive groups with fixed point free involutions

Demonstrated these groups lack nontrivial abelian normal subgroups

Enhanced understanding of the structure of sharply 2-transitive groups

Abstract

We give an explicit construction of sharply $2$-transitive groups with fixed point free involutions and without nontrivial abelian normal subgroup.