A 3-local characterization of Co_2

TL;DR

This paper provides a new characterization of the Conway group Co_2 using local subgroup data, specifically focusing on the centralizer of an element of order 3 and fusion properties.

Contribution

It introduces a 3-local characterization of Co_2 based on centralizer and fusion data, offering a novel approach to understanding this sporadic simple group.

Findings

Characterization of Co_2 via centralizer of order 3 element

Identification of fusion data specific to Co_2

Enhanced understanding of Co_2's local subgroup structure

Abstract

Conway's second largest simple group, $\Co_2$, is characterized by the centralizer of an element of order 3 and certain fusion data.