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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

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