2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/128443We 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 $ϕ^2$.13 pages, 0 figures; second version: bibliography and references corrected;Group Theory20J06; 20E18text