Successive Approximation of p-Class Towers
Daniel C. Mayer · Advances in Pure Mathematics · 2017
Let F be a number field and p be a prime.In the successive approximation theorem, we prove that, for each integer 1 n ≥ , finitely many candidates for the Galois group G n p F of the nth stage ( ) n p cc 1 G = , and establishing a general theorem on the connection between the p-class towers of a number field F and of an unramified abelian p-extension E F , we are able to provide a theoretical proof of the realization of certain 3-groups S with maximal class by 3-tower groups 3 G E ∞ of dihedral fields E with degree 6, which could not be realized up to now.