On the homology of a free nilpotent group of class 2

Let G be a free nilpotent group of class 2, and let G be a free nilpotent Lie ring of class 2 with the same number of free generators. For G a free resolution is constructed which as a graded ZG-module is isomorphic to ZGxΛ(G), where ZG is the group ring of the group G and Λ(G) is the exterior algebra of the ring G. As a consequence of the basic construction an isomorphism HnG≅HnG of integral homology is derived