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 this component is cyclic.
Bibliographical noteThe research of the first author was partially supported by NSA Young Investigator Grant H98230-14-1-0312 and was supported by an AMS-Simons grant which allowed for travel related to this work.
- Fusion systems
- Sporadic groups
- Involution centralizer