A limit approach to group homology

الأصل · EN

In this paper, we consider for any free presentation G = F/R of a group G the coinvariance H₀(G,Rab⊗ ⁿ) of the n-th 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 H₀(G,Rab⊗ ⁿ), 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).