Fusion systems with some sporadic J-components
arXiv:1605.04615 · doi:10.1016/j.jalgebra.2017.06.022
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.
v2: minor corrections in response to anonymous referee report; v3: Theorem 1.2 has been removed due to a error in Lemma 8.22 of v2. The results of v2, Sect. 3 and 8 will appear elsewhere. Additional substantial fixes