Minimal generation of transitive permutation groups

TL;DR

This paper provides an explicit estimate for the constant in a known bound on the number of generators needed for transitive permutation groups of degree d, refining previous asymptotic results.

Contribution

The paper explicitly determines the constant c in the bound for generating transitive permutation groups, improving understanding of their minimal generating sets.

Findings

Explicit estimate of the constant c

Refinement of previous asymptotic bounds

Enhanced understanding of group generation complexity

Abstract

It is proved in [21] that there is a constant $c$ such that each transitive permutation group of degree $d\ge 2$ can be generated by $\lfloor cd/\sqrt{\log{d}}\rfloor$ elements. In this paper, we explicitly estimate $c$.