A limit approach to group homology

In this paper, we consider for any free presentation G=F/R of a group G the coinvariance of the nth tensor power of the relation module Rab and show that the homology group H2n(G,Z) may be identified with the limit of the groups , where the limit is taken over the category of these presentations of G. We also consider the free Lie ring generated by the relation module Rab, in order to relate the limit of the groups γnR/[γnR,F] to the n-torsion subgroup of H2n(G,Z).