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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

The spectral sequence of a finite group extension stops


Author: Leonard Evens
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
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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.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1975-0430024-X
Keywords: Lyndon-Hochschild-Serre, spectral sequence, group cohomology, Tor
Article copyright: © Copyright 1975 American Mathematical Society