Andy Chermak

Fusion systems and localities

Abstract. We introduce a category of objective partial groups, of which the "linking
systems" and "p-local finite groups" of Broto, Levi and Oliver, the "transporter systems"
of Oliver and Ventura, and the "F-localities" of Puig are examples. As an application, we
show that if F is a saturated fusion system over a finite p-group then there exists a centric
linking system L having F as its fusino system, and that L is unique up to isomorphism.
The proof relies on the classification of the finite simple groups in an indirect and - for that
reason - perhaps ultimately removable way.