The rank of fusion systems

In the early 1990s, Puig created his theory of fusion systems as a tool in modular representation theory. Later, Broto, Levi and Oliver used this theory to provide a formal setting for and prove results about the $$p$$p-completed classifying spaces of finite groups. Aschbacher also started a program to establish a local theory of fusion systems similar to the local theory of finite groups. In this paper, we define the notion of ranks for fusion systems which imitates the notion of $$p$$p-local ranks for finite groups and prove some results about weakly normal subsystems and factor systems.