Fusion systems and localities

By A. Chermak. 2013

118 citations recorded by the source corpus.

We introduce 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 $${\mathcal{F}}$$F-localities of Puig are examples, as are groups in the ordinary sense. As an application we show that if $${\mathcal{F}}$$F is a saturated fusion system over a finite p-group then there exists a centric linking system $${\mathcal{L}}$$L having $${\mathcal{F}}$$F as its fusion system, and that $${\mathcal{L}}$$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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9607e22ae6310be60bc0e0d31859f3128a8368db