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