Comparison of the Discrete and Continuous Cohomology Groups of a Pro-$p$ Group

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dc.creatorFernandez-Alcober, Gustavo A.
dc.creatorKazachkov, Ilya V.
dc.creatorRemeslennikov, Vladimir N.
dc.creatorSymonds, Peter
dc.date2007-01-25
dc.date2007-05-07
dc.date.accessioned2026-07-07T07:59:38Z
dc.date.available2026-07-07T07:59:38Z
dc.descriptionWe address the following question. For which finitely generated pro-$p$ groups the comparison map $ϕ^2:H_{cont}^{2}(P,\F_p) \to H_{disc}{2}(P,\F_p)$ is an isomorphism? We prove that if $P$ is not finitely presented then $ϕ^2$ is not surjective. Furthermore, if $P$ is finitely presented $ϕ^2$ is an isomorphism if and only if the comparison map $ϕ_2:H^{disc}_{2}(P, \F_p) \to H^{cont}_{2}(P, \F_p)$ of second homology groups is an isomorphism. This is the content of Theorem A. The second main result of the paper is Theorem B, which gives an explicit construction of a cochain from the kernel of $ϕ^2$.
dc.description13 pages, 0 figures; second version: bibliography and references corrected;
dc.identifierhttps://arxiv.org/abs/math/0701737
dc.identifierhttp://arxiv.org/abs/math/0701737
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/128443
dc.subjectGroup Theory
dc.subject20J06; 20E18
dc.titleComparison of the Discrete and Continuous Cohomology Groups of a Pro-$p$ Group
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