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.

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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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     title = {The {Cohomology} of {Pro-}$p${-Groups} with {Group} {Ring} {Coefficients} and {Virtual} {Poincare} {Duality}},
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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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