It is shown that for certain discrete p-perfect groups G, in particular for
all p-perfect finite groups and certain groups of finite virtual cohomolog
ical dimension, the loop space on the p-completed classifying space Omega B
G(p)(A) is a retract of the loop space on the p-completion of a certain fin
ite complex. For those finite virtual cohomological dimension groups where
the author's methods apply, a bound on the dimension of such a complex is p
rovided.