@techreport{42de11e203a54b7b9155cdf7dd05fd00,

title = "Fusion systems with Benson-Solomon components",

abstract = "The Benson-Solomon systems comprise the one currently known family of simple exotic fusion systems at the prime $2$. We show that if $\mathcal{F}$ is a fusion system on a $2$-group having a Benson-Solomon subsystem $\mathcal{C}$ which is subintrinsic and maximal in the collection of components of involution centralizers, then $\mathcal{C}$ is a component of $\mathcal{F}$, and in particular, $\mathcal{F}$ is not simple. This is one part of the proof of a Walter's Theorem for fusion systems, which is itself a major step in a program for the classification of a wide class of simple fusion systems of component type at the prime $2$.",

keywords = "math.GR, 20D20, 20D05",

author = "Ellen Henke and Justin Lynd",

note = "This project has received funding from the European Union{\textquoteright}s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 707758",

year = "2018",

month = jun,

day = "5",

language = "English",

series = "arXiv",

type = "WorkingPaper",

}