Symmetric Generation of $M_{22}$

TL;DR

This paper provides a computer-free proof demonstrating that the Mathieu group M22 can be obtained as a homomorphic image of a specific progenitor group, using a factorization with three relations.

Contribution

It introduces a novel, computer-free proof method for deriving M22 from a progenitor group, enhancing understanding of its algebraic structure.

Findings

M22 is a homomorphic image of 2^{*14}:L_3(2)

The proof uses three specific relations

The approach avoids computational methods

Abstract

We give a computer-free proof that the Mathieu group $M_{22}$ is a homomorphic image of the progenitor $2^{\ast 14}:L_3(2)$ factorized by three relations.