Abstract
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].
Similar content being viewed by others
References
S. MacLane, Homology, Reprint of the 1975 edition. Classics in Mathematics. Springer-Verlag, Berlin (1995).
S. Takasu, “Relative homology and relative cohomology theory of groups,” J. Fac. Sci. Univ. Tokyo. Sect. I, 8, 75–110 (1959).
S. Takasu, “On the change of rings in the homological algebra,” J. Math. Soc. Japan, 9, 315–329 (1957).
Author information
Authors and Affiliations
Additional information
__________
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 43, Topology and Its Applications, 2006.
Rights and permissions
About this article
Cite this article
Katamadze, R.D. Homology and cohomology groups of the group homomorphism. J Math Sci 152, 323–329 (2008). https://doi.org/10.1007/s10958-008-9071-x
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-008-9071-x