Homology and cohomology groups of the group homomorphism

As is known, the homology and cohomology Massa-Takasu groups for pairs of groups (G, H) are defined by the embedding f: H → G, H < G [2]. In our case, these definitions are extended to an arbitrary group homomorphism φ: Π → G. In particular, we define homology and cohomology groups of the nth order for the homomorphism φ, and if Π = H, we obtain the known theory [2]. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 43, Topology and Its Applications, 2006.