UNSTABLE SPLITTINGS OF CLASSIFYING SPACES OF P-COMPACT GROUPS

                              D.Notbohm

Dwyer and Wilkerson gave a definition 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 enjoy most properties of 
compact Lie groups 
establishes a program for the classification of these objects. Following the 
classification of connected compact 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 \pcg\ splits into a product if the normalizer
of the maximal torus does.