Sharply 2-transitive groups in characteristic 0

TL;DR

This paper constructs new examples of sharply 2-transitive groups in characteristic 0 that lack non-trivial abelian normal subgroups, answering a longstanding open question in group theory.

Contribution

It provides the first known examples of such groups, expanding understanding of the structure of sharply 2-transitive groups in characteristic 0.

Findings

Constructed sharply 2-transitive groups in characteristic 0

These groups have no non-trivial abelian normal subgroups

Groups act sharply 2-transitively on their involutions by conjugation

Abstract

We construct sharply 2-transitive groups of characteristic 0 without non-trivial abelian normal subgroup. These groups act sharply 2-trnaisitvely by conjugation on their involutions. This answers a longstanding open question.