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Jacobson, M.J. (1998) Experimental Results on Class Groups of Real Quadratic Fields. In: Buhler, J.P., Ed., Algorithmic Number Theory, ANTS 1998, Lecture Notes in Computer Science, Vol. 1423, Springer, Berlin, Heidelberg.
https://doi.org/10.1007/BFb0054885

has been cited by the following article:

• TITLE: Successive Approximation of p-Class Towers

  AUTHORS: Daniel C. Mayer

  KEYWORDS: p-Class Towers, Galois Groups, Second p-Class Groups, Abelian Type Invariants of p-Class Groups, p-Transfer Kernel Types, Artin Limit Pattern, Quadratic Fields, Unramified Cyclic Extensions of Degree p, Dihedral Fields of Degree 2p, Finite p-Groups, Maximal Nilpotency Class, Maximal Subgroups, Polycyclic Pc-Presentations, Commutator Calculus, Central Series

  JOURNAL NAME: Advances in Pure Mathematics, Vol.7 No.12, December 21, 2017

  ABSTRACT: Let F be a number field and p be a prime. In the successive approximation theorem, we prove that, for each integer n ≥ 1, finitely many candidates for the Galois group of the nth stage of the p-class tower over F are determined by abelian type invariants of p-class groups C1pE of unramified extensions E/F with degree [E : F] = pn-1. Illustrated by the most extensive numerical results available currently, the transfer kernels (TE, F) of the p-class extensions TE, F : C1pF → C1pE from F to unramified cyclic degree-p extensions E/F are shown to be capable of narrowing down the number of contestants significantly. By determining the isomorphism type of the maximal subgroups S G of all 3-groups G with coclass cc(G) = 1, 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 of dihedral fields E with degree 6, which could not be realized up to now.