Sharply 3-transitive groups

TL;DR

This paper constructs the first examples of sharply 3-transitive groups that do not originate from near fields, showing a new class of such groups with unique stabilizer properties.

Contribution

It introduces the first sharply 3-transitive groups not derived from near fields, expanding the understanding of permutation group structures.

Findings

Constructed new sharply 3-transitive groups without near field origin

Point stabilizers lack nontrivial abelian normal subgroups

Demonstrated existence of groups with novel transitivity properties

Abstract

We construct the first sharply $3$-transitive groups not arising from a near field, i.e. point stabilizers have no nontrivial abelian normal subgroup.