Centralisers of Subsystems of Fusion Systems

Jason Semeraro

Research output: Contribution to journalArticle (Academic Journal)

Abstract

When $(S,\mathcal{F},\mathcal{L})$ is a $p$-local finite group and $(T,\mathcal{E},\mathcal{L}_0) \unlhd (S,\mathcal{F},\mathcal{L})$ we define an $S$-centraliser $C_S(\mathcal{L}_0)$ of $\mathcal{L}_0$ in $S$ and observe that this is equivalent to a definition of $C_S(\mathcal{E})$ given by Aschbacher. We also appeal to a result of Gross to give a new proof that there is a unique fusion system $C_{\mathcal{F}}(\mathcal{E})$ on $C_S(\mathcal{E})$.
Original languageEnglish
JournalarXiv
Publication statusPublished - 20 Feb 2014

Bibliographical note

11 pages

Keywords

  • math.GR

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