Demuškin groups, Galois modules, and the Elementary Type Conjecture

Let p be a prime and F(p) the maximal p-extension of a field F containing a primitive pth root of unity. We give a new characterization of Demuškin 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).