Geodesic
The Cohomology of Pro-$p$-Groups with Group Ring Coefficients and Virtual Poincare Duality
Matematičeskie zametki, Tome 78 (2005) no. 6, pp. 853-863 
A. A. Korenev. The Cohomology of Pro-$p$-Groups with Group Ring Coefficients and Virtual Poincare Duality. Matematičeskie zametki, Tome 78 (2005) no. 6, pp. 853-863. http://geodesic.mathdoc.fr/item/MZM_2005_78_6_a4/
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     author = {A. A. Korenev},
     title = {The {Cohomology} of {Pro-}$p${-Groups} with {Group} {Ring} {Coefficients} and {Virtual} {Poincare} {Duality}},
     journal = {Matemati\v{c}eskie zametki},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2005_78_6_a4/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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