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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
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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


References [Enhancements On Off] (What's this?)

  • [1] H. Cartan and S. Eilenberg, Homological algebra, Princeton Univ. Press, Princeton, N. J., 1956. MR 17, 1040. MR 0077480 (17:1040e)
  • [2] A. Grothendieck, Éléments de géométrie algébrique. IV: Études locale de schémas et des morphismes de schémas. I, Inst. Hautes Études Sci. Publ. Math. No. 20 (1964). MR 30 #3885. MR 0173675 (30:3885)
  • [3] R. C. Lyndon, The cohomology theory of group extensions, Duke Math. J. 15 (1948), 271-292. MR 10, 10. MR 0025468 (10:10c)
  • [4] B. Pareigis, Zur Kohomologie endlich erzeugter abelscher Gruppen, Bayer. Akad. Wiss. Math.-Natur. K1. S.-B. 1967, Abt. II, 177-193. MR 0238959 (39:319)

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DOI: https://doi.org/10.1090/S0002-9939-1970-0257184-9
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

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