Unstable splittings of classifying spaces of p-compact groups

Abstract. Dwyer and Wilkerson gave a denition of a p{compact group, which is a loop space with certain properties and a good generalisation of the notion of compact Lie groups in terms of classifying spaces and homotopy theory; e.g. every p{compact group has a maximal torus, a normalizer of the maximal torus and a Weyl group. The believe or hope that p{compact groups enjoys most properties of compact Lie groups establishes a program for the classication of these objects. Following the classication of compact connected Lie groups, one step in this program is to show that every simply connected p{compact group splits into a product of simply connected simple p{compact groups. The proof of this splitting theorem is based on the fact that every classifying space of a p{compact group splits into a product if the normalizer of the maximal torus does. 1. Introduction. A loop space is a triple X = (X;BX; e: ΩBX ’−! X), where X and BX are toplogical spaces, where BX is pointed, and where e is a homotopy equivalenc