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The narrow class groups of the ℤ17- and ℤ19-extensions over the rational field

The narrow class groups of the ℤ17- and ℤ19-extensions over the rational field Let p be either 17 or 19, let ℤ p denote the ring of p-adic integers, and let l be a prime number which is a primitive root modulo p 2. We shall prove, with the help of a computer, that the l-class group of the ℤ p -extension over the rational field is trivial. We shall also prove the triviality of the narrow 2-class group of the same ℤ p -extension. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Springer Journals

The narrow class groups of the ℤ17- and ℤ19-extensions over the rational field

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References (15)

Publisher
Springer Journals
Copyright
Copyright © 2009 by Mathematisches Seminar der Universität Hamburg and Springer
Subject
Mathematics; Geometry ; Topology; Number Theory; Combinatorics; Differential Geometry; Algebra
ISSN
0025-5858
eISSN
1865-8784
DOI
10.1007/s12188-009-0030-3
Publisher site
See Article on Publisher Site

Abstract

Let p be either 17 or 19, let ℤ p denote the ring of p-adic integers, and let l be a prime number which is a primitive root modulo p 2. We shall prove, with the help of a computer, that the l-class group of the ℤ p -extension over the rational field is trivial. We shall also prove the triviality of the narrow 2-class group of the same ℤ p -extension.

Journal

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg – Springer Journals

Published: Oct 27, 2009

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