### 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 $2$.

Original language | English |
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Publication status | Submitted - 5 Jun 2018 |

### Publication series

Name | arXiv |
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### Keywords

- math.GR
- 20D20, 20D05

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## Profiles

### Ellen Henke

- School of Natural & Computing Sciences, Mathematical Science - Senior Lecturer
- Mathematical Sciences (Research Theme)

Person: Academic

## Cite this

Henke, E., & Lynd, J. (2018).

*Fusion systems with Benson-Solomon components*. (arXiv).