Fusion systems with some sporadic J-components

TL;DR

This paper advances the classification of certain 2-fusion systems by analyzing those with J-components resembling sporadic groups, assuming their centralizers are cyclic, thus contributing to Aschbacher's program.

Contribution

It classifies 2-fusion systems with J-components isomorphic to sporadic groups under cyclic centralizer assumptions, advancing the understanding of J-component type fusion systems.

Findings

Classified 2-fusion systems with specific sporadic J-components

Established cyclic centralizer condition as key assumption

Extended the classification framework for fusion systems

Abstract

Aschbacher's program for the classification of simple fusion systems of "odd" type at the prime 2 has two main stages: the classification of 2-fusion systems of subintrinsic component type and the classification of 2-fusion systems of J-component type. We make a contribution to the latter stage by classifying 2-fusion systems with a J-component isomorphic to the 2-fusion systems of several sporadic groups under the assumption that the centralizer of such a component is cyclic.