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 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 \(\Lambda_\mathcal{F}\).