Fusion systems with 2-small components

Abstract

We show that there are no odd simple 2-fusion systems F in which the centralizer of some fully centralized involution contains a component C that is the 2-fusion system of a simple group K such that C is J-maximal or maximal and subintrinsic in C(F), as appropriate, and such that K is of Lie type over the field of order 2, but not Spₙ(2) or F₄(2); or K is one of many sporadic groups; or K is PΩ⁺₈(3).

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