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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Duality and local group cohomology


Author: P. R. Hewitt
Journal: Proc. Amer. Math. Soc. 126 (1998), 1909-1914
MSC (1991): Primary 20J05
MathSciNet review: 1468193
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Abstract: Let $G$ be a group, let $k$ be a field, and let ${\mathcal{L}}$ be a local system - an upwardly directed collection of subgroups whose union is $G$. In this paper we give a short, elementary proof of the following result: If either $A$ is a $k$-$kG$-bimodule, or else $k$ is finite dimensional over its center, then $\operatorname{Ext}^{*}_{G}(A,B^{\vee }) =\varprojlim _{L\in\mathcal{L}} \operatorname{Ext}^{*}_{L}(A,B^{\vee })$. From this we deduce as easy corollaries some recent results of Meierfrankenfeld and Wehrfritz on the cohomology of a finitary module.


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Additional Information

P. R. Hewitt
Affiliation: Department of Mathematics, University of Toledo, Toledo, Ohio 43606

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04543-2
PII: S 0002-9939(98)04543-2
Received by editor(s): December 12, 1996
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1998 American Mathematical Society