An identification theorem for the sporadic simple groups F_2 and M(23)

TL;DR

This paper presents a new identification theorem for the sporadic simple groups M(23) and F_2 based on the structure of centralizers of elements of order 3, advancing understanding of their unique properties.

Contribution

It introduces a novel identification method for these groups using local subgroup structures, specifically centralizers of elements of order 3.

Findings

Successfully identified M(23) and F_2 using centralizer structures

Provided new characterization theorems for these sporadic groups

Enhanced the classification framework for sporadic simple groups

Abstract

We identify the sporadic groups M(23) and F_2 from the approximate structure of the centralizer of an element of order 3.