The rank of fusion systems

Abstract

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 \(p\)-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 \(p\)-local ranks for finite groups and prove some results about weakly normal subsystems and factor systems.