Minimal characteristic bisets for fusion systems

Abstract

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