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This article is cited in 3 scientific papers (total in 3 papers)
The Cohomology of Pro-$p$-Groups with Group Ring Coefficients and Virtual Poincare Duality
A. A. Korenev Belarusian State University
Abstract:
The relationship between the group-theoretic properties of a pro-$p$-group $G$ and the $G$-module structure of the group $H^n(G,\mathbb F_q[[G]])$ is studied. A necessary and sufficient condition for a pro-$p$-group $G$ to contain an open Poincare subgroup of dimension $n$ is obtained. This condition does not require that $G$ have finite cohomological dimension and, therefore, applies to groups with torsion. Results concerning the possible values of $\dim_{\mathbb F_p}H^n(G,\mathbb F_p[[G]])$ are also obtained.
Received: 29.04.2004
Citation:
A. A. Korenev, “The Cohomology of Pro-$p$-Groups with Group Ring Coefficients and Virtual Poincare Duality”, Mat. Zametki, 78:6 (2005), 853–863; Math. Notes, 78:6 (2005), 791–800
Linking options:
https://www.mathnet.ru/eng/mzm2657https://doi.org/10.4213/mzm2657 https://www.mathnet.ru/eng/mzm/v78/i6/p853
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Abstract page: | 334 | Full-text PDF : | 105 | References: | 27 | First page: | 1 |
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