CENTERS AND FINITE COVERINGS OF FINITE LOOP SPACES
J. M. Moeller and D. Notbohm

Abstract: The homotopy theoretic analogue of a compact Lie group is
a p-compact group , i.e a space X with finite mod-p cohomology
and an loop structure given by an equivalence of the form
X\simeq \Omega BX. The `classifying space' BX has to be a p--complete 
space. We are concerned with the notions of  centers and finite coverings
of p-compact groups. In particular , we prove in this category 
two well known results for compact Lie groups; namely that the center 
of a connected p-compact group is finite iff the fundamental group is 
finite and that every p-compact connected group has a finite covering 
which is a product of a simply connected p-compact group and 
a torus. The latter statement also translates to connected finite loop spaces.