Primitive permutation groups as products of point stabilizers

TL;DR

This paper proves that any finite primitive permutation group with a non-trivial point stabilizer can be expressed as a product of a logarithmic number of point stabilizers, establishing a universal bound.

Contribution

It introduces a universal constant bounding the number of point stabilizers needed to express such groups as products.

Findings

Bound of c log n point stabilizers for primitive groups

Universal constant c independent of group size

Structural insight into primitive permutation groups

Abstract

We prove that there exists a universal constant $c$ such that any finite primitive permutation group of degree $n$ with a non-trivial point stabilizer is a product of no more than $c\log n$ point stabilizers.