The spectral sequence of a finite group extension stops
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- by Leonard Evens PDF
- Trans. Amer. Math. Soc. 212 (1975), 269-277 Request permission
Abstract:
It is proved that if G is a finite group, H a normal subgroup, and A a finitely generated G-module, then both the cohomology and homology spectral sequences for the group extension stop in a finite number of stops. A lemma about ${\operatorname {Tor}}(M,N)$ as a module over $R \otimes S$ is proved. Two spectral sequences of Hochschild and Serre are shown to be the same.References
- Leonard Evens, The cohomology ring of a finite group, Trans. Amer. Math. Soc. 101 (1961), 224–239. MR 137742, DOI 10.1090/S0002-9947-1961-0137742-1
- Saunders MacLane, Homology, 1st ed., Die Grundlehren der mathematischen Wissenschaften, Band 114, Springer-Verlag, Berlin-New York, 1967. MR 0349792
- G. Hochschild and J.-P. Serre, Cohomology of group extensions, Trans. Amer. Math. Soc. 74 (1953), 110–134. MR 52438, DOI 10.1090/S0002-9947-1953-0052438-8
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 212 (1975), 269-277
- MSC: Primary 18G40; Secondary 20J05
- DOI: https://doi.org/10.1090/S0002-9947-1975-0430024-X
- MathSciNet review: 0430024