### Abstract

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

### Publication series

Name | arXiv |
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### Fingerprint

### Keywords

- math.GR
- 20D20, 20D05

### Cite this

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

**Fusion systems with Benson-Solomon components.** / Henke, Ellen; Lynd, Justin.

Research output: Working paper

}

TY - UNPB

T1 - Fusion systems with Benson-Solomon components

AU - Henke, Ellen

AU - Lynd, Justin

N1 - This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 707758

PY - 2018/6/5

Y1 - 2018/6/5

N2 - 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 $2$.

AB - 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 $2$.

KW - math.GR

KW - 20D20, 20D05

M3 - Working paper

T3 - arXiv

BT - Fusion systems with Benson-Solomon components

ER -