A principal ideal theorem in the genus field

DOI10.2748/TMJ/1178242555zbMath0243.12003OpenAlexW2043093750MaRDI QIDQ2554359

Fumiyuki Terada

Publication date: 1971

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1178242555

Mathematics Subject Classification ID

Class field theory (11R37) Iwasawa theory (11R23)

Related Items (13)

Invariant generalized ideal classes -- structure theorems for \(p\)-class groups in \(p\)-extensions ⋮ Sur une question de capitulation ⋮ Integral representations for the alternating groups ⋮ Unnamed Item ⋮ 3-Principalization over S3 -fields ⋮ Ostrowski quotients for finite extensions of number fields ⋮ On the structure of the idele groups of algebraic number fields. II ⋮ Capitulation in the absolutely abelian extensions of some number fields. II ⋮ ON THE STRONGLY AMBIGUOUS CLASSES OF 𝕜/ℚ(i) WHERE $\mathds{k} = {\mathbb Q}(\sqrt{2p_{1}p_{2}, i})$ ⋮ Group Theory and the Capitulation Problem for Some Number Fields ⋮ Principal ideal theorems in the genus field for absolutely abelian extensions ⋮ Imaginary bicyclic biquadratic fields with the real quadratic subfield of class-number one ⋮ The application of the principal ideal theorem to p-groups

Cites Work

• A generalization of the principal ideal theorem
• A generalized principal ideal theorem and a proof of a conjecture of Deuring
• On a generalization of the principal ideal theorem
• Zur Geschlechtertheorie in quadratischen Zahlkörpern
• On the Class Number of a Relatively Cyclic Number Field
• Zur Geschlechtertheorie in abelschen Zahlkörpern
• Unnamed Item

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