Abstract: The main topic of this paper is to generalize the problem of Beckmann-Black for pro�nite groups. We introduce the Beckmann-Black problem for complete systems of �finite groups and for unramified extensions. We prove that every Galois extension of profi�nite abelian group over a ψ-free fi�eld is the specialization of some tower of regular Galois extensions of the same group.
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