An Algebraic Model for Finite Loop Spaces

A p-local compact group consists of a discrete p-toral group S, together with a fusion system and a linking system over S which define a classifying space having very nice homotopy properties. We prove here that if some finite regular cover of a space Y is the classifying space of a p-local compact group, then so is Y^p . Together with earlier results by Dwyer and Wilkerson and by the authors, this implies as a special case that a finite loop space determines a p-local compact group at each prime p.