Note on the homology of a fiber product of groups
Author:
G. S. Rinehart
Journal:
Proc. Amer. Math. Soc. 24 (1970), 548-552
MSC:
Primary 18.20
DOI:
https://doi.org/10.1090/S0002-9939-1970-0257184-9
MathSciNet review:
0257184
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: Spectral sequences are derived for the homology and cohomology of a fiber product of groups with coefficients in a tensor product module. These generalize the Hochschild-Serre spectral sequences, and, in the case of a full product of groups, give Künneth formulas. The latter are used to make easy explicit computations of the homology and cohomology of an arbitrary finitely generated
- Henri Cartan and Samuel Eilenberg, Homological algebra, Princeton University Press, Princeton, N. J., 1956. MR 0077480
- A. Grothendieck, Éléments de géométrie algébrique. IV. Étude locale des schémas et des morphismes de schémas. I, Inst. Hautes Études Sci. Publ. Math. 20 (1964), 259 (French). MR 173675
- Roger C. Lyndon, The cohomology theory of group extensions, Duke Math. J. 15 (1948), 271–292. MR 25468
- Bodo Pareigis, Zur Kohomologie endlich erzeugter abelscher Gruppen, Bayer. Akad. Wiss. Math.-Natur. Kl. S.-B. 1967 (1968), no. Abt. II, 177–193 (1968) (German). MR 238959
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 18.20
Retrieve articles in all journals with MSC: 18.20
Additional Information
Keywords:
Homology of groups,
cohomology of groups,
fiber product of groups,
Hochschild-Serre spectral sequence,
Künneth formula,
homology of abelian groups,
cohomology of abelian groups,
universal coefficient theorems
Article copyright:
© Copyright 1970
American Mathematical Society