The exact spread of M23 is 8064

TL;DR

This paper proves the exact size of a maximal set of elements in the Mathieu group M23 with a specific generative property, establishing a precise combinatorial characterization.

Contribution

It establishes that the largest such set in M23 has exactly 8064 elements, providing a precise combinatorial and group-theoretic result.

Findings

The maximum size of a set with the property is 8064.

Any larger set does not have the property.

The property involves a universal element generating the group with each set element.

Abstract

We show that if {x1,...,x8064} is a set of distinct non-trivial elements of the sporadic simple Mathieu group M23 then there exists an element y such that {y,x_i} generates the whole group for every 0<i<8065 and that no larger set of distinct elements of M23 has this property.