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 K[s,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 K[s,M]/K. As application we prove that the ramification subgroup of the absolute Galois group of K with the upper index v acts trivially on K[s,M] iff v>e K (M+s/(p-1))-(1-δ 1s )/p, where e K is the ramification index of K and δ 1s is the Kronecker symbol.