Generating minimally transitive permutation groups

TL;DR

This paper improves upper bounds on the number of elements needed to generate minimally transitive permutation groups of degree n, advancing understanding of their minimal generating sets.

Contribution

It provides tighter upper bounds on the minimal number of generators for minimally transitive permutation groups, refining previous results.

Findings

Improved upper bounds in terms of n

Enhanced understanding of minimal generating sets

Refined theoretical limits on group generation

Abstract

We improve the upper bounds (in terms of $n$) in [9] and [13] on the minimal number of elements required to generate a minimally transitive permutation group of degree $n$.