A 3-local characterization of M_12 and SL_3(3)

TL;DR

This paper characterizes the sporadic simple group M12 and the simple group SL_3(3) using their 3-local structures and provides a graph-theoretic analogue of this characterization.

Contribution

It offers a new local characterization of M12 and SL_3(3) and introduces a graph-theoretic analogue of this theorem.

Findings

Identification of M12 and SL_3(3) via 3-local structures

Development of a graph-theoretic analogue of the characterization

Enhanced understanding of the local properties of these groups

Abstract

We identify the sporadic simple group $\mathrm{M}_{12}$ and the simple group $\mathrm{SL}_3(3)$ from some part of their 3-local structure and give a graph theoretic analogue of the resulting theorem.