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On Modules of Trivial Cohomology over a Finite Group, II (Finitely Generated Modules)

Published online by Cambridge University Press:  22 January 2016

Tadasi Nakayama
Tadasi Nakayama*
Affiliation:
Nagoya University
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Let G be a finite group. A(left) G-module A of G is said to be of trivial cohomology when Hn(H, A)= 0 for all rational integers n and for all subgroups H of G. The main purpose of the present note is to determine the structure of finitely generated G-modules of trivial cohomology, which turns out to be remarkably simple (See Theorem 1 and Corollary 3 below). We prove also an (easy) localization theorem for cohomological triviality.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 12 , December 1957 , pp. 171 - 176
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1957

References

[1] Cartan, H.-Eilenberg, S., Homological Algebra, Princeton 1956.Google Scholar
[2] Eilenberg, S., Homological dimension and syzygies, Ann. Math., 64 (1956), 328–336.Google Scholar
[3] Higman, , Modules with a group of operators, Duke Math. Jour., 21 (1954), 369–376.CrossRefGoogle Scholar
[4] Kasch, F., Grundlagen einer Theorie der Frobeniuserweiterungen, Math. Ann., 127 (1954), 453–474.Google Scholar
[5] Nagao, H.-Nakayama, T., On the structure of (M0)- and (Mu)-modules, Math. Zeits, 59 (1953), 164–170.CrossRefGoogle Scholar
[6] Serre, J.-P., Sur la dimension homologique des anneaux et des modules Noethériens, Proc. Intern. Symposium, Tokyo 1955.Google Scholar