Minimal characteristic bisets for fusion systems

We show that every saturated fusion system FF has a unique minimal FF-characteristic biset ΛFΛF. We examine the relationship of ΛFΛF 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 FF-characteristic biset, and more generally, any centric linking system can be identified with the FF-centric part of ΛFΛF as bisets. We explore the grouplike properties of ΛFΛF, and conjecture an identification of normalizer subsystems of FF with subbisets of ΛFΛF.