Minimal characteristic bisets for fusion systems

We show that every saturated fusion system $\mathcal{F}$ has a unique minimal $\mathcal{F}$-characteristic biset $\Lambda_\mathcal{F}$. We examine the relationship of $\Lambda_\mathcal{F}$ with other concepts in $p$-local finite group theory: In the case of a constrained fusion system, the...

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Veröffentlicht in:	arXiv.org 2014-03
Hauptverfasser:	Gelvin, Matthew, Sune Precht Reeh
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Sprache:	eng
Schlagworte:	Group theory Subsystems
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description	We show that every saturated fusion system $\mathcal{F}$ has a unique minimal $\mathcal{F}$-characteristic biset $\Lambda_\mathcal{F}$. We examine the relationship of $\Lambda_\mathcal{F}$ with other concepts in $p$-local finite group theory: In the case of a constrained fusion system, the model for the fusion system is the minimal $\mathcal{F}$-characteristic biset, and more generally, any centric linking system can be identified with the $\mathcal{F}$-centric part of $\Lambda_\mathcal{F}$ as bisets. We explore the grouplike properties of $\Lambda_\mathcal{F}$, and conjecture an identification of normalizer subsystems of $\mathcal{F}$ with subbisets of $\Lambda_\mathcal{F}$.
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title	Minimal characteristic bisets for fusion systems
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