This paper shows that p-compact groups have well defined
centers with all the usual proprties of centers in the Lie
case. The center is a maximal central monomorphism, and
the quotient mod the center is shon to exists as a p-compact group.
This "adjoint" from in turn has trivial center if the original
p-compact group is connected.
The usual calculation of hte center in terms of the root system /Weyl group
actions are proved.
Finally, it's shown that the "algebraic" center above is exactly the
"geometric" or "homotopy" center, defined as \loop(Map(BX,BX)_{Id},
thus generalizing the work of JMO in the Lie group case.