# Fusion systems with Benson-Solomon components

Ellen Henke, Justin Lynd

Research output: Working paper

## 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 Submitted - 5 Jun 2018

### Publication series

Name arXiv

• math.GR
• 20D20, 20D05