Suppose K is a finite field extension of Q(P) containing a p(M)-th primitive root of unity. For 1 = s p denote by Ks, M the maximal p-extension of K with the Galois group of period p(M) and nilpotent class s. We apply the nilpotent Artin-Schreier theory together with the theory of the field-of-norms functor to give an explicit description of the Galois groups of Ks, M/K. As application we prove that the ramification subgroup of the absolute Galois group of K with the upper index upsilon acts trivially on Ks, M iff upsilon e(K)(M + s/(p-1))-(1-delta(1s))/p, where e(K) is the ramification index of K and delta(1s) is the Kronecker symbol.
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