**
G. Ellis**

##
A Magnus-Witt Type Isomorphism for Non-Free Group

**abstract:**

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 G_{ab}. We end the paper with
some related remarks about precrossed modules and partial Lie algebras.