Affiliation:
1. Naglergasse 53, 8010 Graz, Austria
Abstract
For a prime p ≥ 2 and a number field K with p-class group of type (p, p) it is shown that the class, coclass, and further invariants of the metabelian Galois group [Formula: see text] of the second Hilbert p-class field [Formula: see text] of K are determined by the p-class numbers of the unramified cyclic extensions Ni|K, 1 ≤ i ≤ p + 1, of relative degree p. In the case of a quadratic field [Formula: see text] and an odd prime p ≥ 3, the invariants of G are derived from the p-class numbers of the non-Galois subfields Li|ℚ of absolute degree p of the dihedral fields Ni. As an application, the structure of the automorphism group [Formula: see text] of the second Hilbert 3-class field [Formula: see text] is analyzed for all quadratic fields K with discriminant -106 < D < 107 and 3-class group of type (3, 3) by computing their principalization types. The distribution of these metabelian 3-groups G on the coclass graphs [Formula: see text], 1 ≤ r ≤ 6, in the sense of Eick and Leedham-Green is investigated.
Publisher
World Scientific Pub Co Pte Lt
Subject
Algebra and Number Theory
Cited by
7 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献