Comparing the order and the minimal number of generators of a transitive permutation group

TL;DR

This paper investigates the relationship between the order and the minimal number of generators of transitive permutation groups, showing that a specific logarithmic ratio diminishes as the degree increases.

Contribution

It establishes a new asymptotic result linking the minimal number of generators and the order of transitive permutation groups as their degree grows.

Findings

The ratio d(G) log|G| / n^2 tends to zero for large n.

Provides asymptotic behavior of generators in transitive groups.

Enhances understanding of group generation complexity.

Abstract

We prove that if $G$ is a transitive permutation group, then $d(G)\log{|G|}/n^{2}$ tends to $0$ as $n$ tends to $\infty$.