Fusion systems with Benson-Solomon components

Ellen Henke, Justin Lynd

Research output: Working paper

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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 languageEnglish
Publication statusSubmitted - 5 Jun 2018

Publication series

NamearXiv

Fingerprint

Fusion
Centralizer
Involution
Subsystem
Theorem

Keywords

  • math.GR
  • 20D20, 20D05

Cite this

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

2018. (arXiv).

Research output: Working paper

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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 $2$.

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