The narrow class groups of the \(\mathbb Z_{17}\)- and \(\mathbb Z_{19}\)-extensions over the rational field

DOI10.1007/s12188-009-0030-3zbMath1214.11125OpenAlexW2115722467MaRDI QIDQ977335

Kuniaki Horie, Mitsuko Horie

Publication date: 21 June 2010

Published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12188-009-0030-3

zbMATH Keywords

Iwasawa theory\(\mathbb Z_p\)-extensionnarrow class group

Mathematics Subject Classification ID

Class numbers, class groups, discriminants (11R29) Iwasawa theory (11R23) Other abelian and metabelian extensions (11R20)

Related Items (8)

Mahler measure and Weber's class number problem in the cyclotomic \(\mathbb Z_p\)-extension of \(\mathbb Q\) for odd prime number \(p\) ⋮ The \(l\)-class group of the \(\mathbb Z_p\)-extension over the rational field ⋮ Height and Weber's class number problem ⋮ The ideal class group of the \(Z_{23}\)-extension over the rational field ⋮ On the 2-part of the class numbers of cyclotomic fields of prime power conductors ⋮ On the Class Numbers in the Cyclotomic Z29- and Z31-Extensions of the Field of Rationals ⋮ Weber’s Class Number One Problem ⋮ Triviality of the ℓ-class groups in -extensions of for split primes p ≡ 1 modulo 4

Cites Work

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• A note on class numbers of algebraic number fields
• Primary components of the ideal class group of the \(\mathbb Z_p\)-extension over \(\mathbb Q\) for typical inert primes
• Class numbers and \(\mathbb Z_p\)-extensions
• Certain primary components of the ideal class group of the \(\mathbb Z_p\)-extension over the rationals
• Ideal Class Groups of Iwasawa-Theoretical Abelian Extensions Over the Rational Field
• The narrow class groups of some Z_p-extensions over the rationals
• Classnumbers and unit signatures

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