  Let \Omega X be the space of Moore loops on a finite, q-connected,
n-dimensional CW complex X, and let R be a subring of Q containing 1/2. Let
p(R) be the least non-invertible prime in R. For a graded R-module M of finite
type, let FM = M / Torsion M. We show that the inclusion of the sub-Lie algebra
P of primitive elements of FH_*(\Omega X;R) induces an isomorphism of Hopf
algebras UP = FH_*(\Omega X;R), provided p(R) > n/q - 1. Furthermore, the
Hurewicz homomorphism induces an embedding of F(\pi_*(\Omega X)\otimes R) in P,
with torsion cokernel. As a corollary, if X is elliptic, then FH_*(\Omega X;R)
is a finitely-generated R-algebra.
