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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
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.

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

  • [E] L. Evens, The cohomology ring of a finite group, Trans. Amer. Math. Soc. 101 (1961), 224-239. MR 25 #1191. MR 0137742 (25:1191)
  • [Mac] S. Mac Lane, Homology, Die Grundlehren der math. Wissenschaften, Band 114, Academic Press, New York; Springer-Verlag, Berlin, 1963. MR 28 #122. MR 0349792 (50:2285)
  • [HS] G. Hochschild and J.-P. Serre, Cohomology of group extensions, Trans. Amer. Math. Soc. 74 (1953), 110-135. MR 14, 619. MR 0052438 (14:619b)

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Keywords: Lyndon-Hochschild-Serre, spectral sequence, group cohomology, Tor
Article copyright: © Copyright 1975 American Mathematical Society

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