A Magnus-witt Type Isomorphism For Non-Free Groups

We use the theory of nonabelian derived functors to prove that certain Baer invariants of a group G are torsion when G has torsion second integral homology. We use this result to show that if such a group has torsion-free abelianisation then the Lie algebra formed from the quotients of the lower central series of G is isomorphic to the free Lie algebra on Gab. We end the paper with some related remarks about precrossed modules and partial Lie algebras.