2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101299Let p be a prime and F(p) the maximal p-extension of a field F containing a primitive p-th root of unity. We give a new characterization of Demuskin groups among Galois groups Gal(F(p)/F) when p=2, and, assuming the Elementary Type Conjecture, when p>2 as well. This characterization is in terms of the structure, as Galois modules, of the Galois cohomology of index p subgroups of Gal(F(p)/F).v2 (20 pages); added theorem characterizing decompositions into free and trivial modules; to appear in J. AlgebraNumber Theory12G05; 20E18text