The 2-rank of the real pure quartic number field \(K= \mathbb{Q}(\sqrt[4]{pd^{2}})\)

DOI10.1216/rmj.2023.53.27MaRDI QIDQ6158188

Mbarek Haynou, Mohammed Taous, Bouchaïb Sodaïgui

Publication date: 31 May 2023

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/journals/rocky-mountain-journal-of-mathematics/volume-53/issue-1/THE-2-RANK-OF-THE-REAL-PURE-QUARTIC-NUMBER-FIELD/10.1216/rmj.2023.53.27.full

zbMATH Keywords

Hilbert symbolclass groupsramificationpure quartic number field class number

Mathematics Subject Classification ID

Quadratic extensions (11R11) Class field theory (11R37) Cubic and quartic extensions (11R16) Class numbers, class groups, discriminants (11R29)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On relative integral bases for pure quartic fields
• The 2-class group of biquadratic fields. II
• A remark on the capitulation problem
• The 2-rank of the class group of some real cyclic quartic number fields
• On the 2-rank and 4-rank of the class group of some real pure quartic number fields
• Fundamental units of real quadratic fields of odd class number
• Sur le rang du 2-groupe de classes de 𝑄({√{𝑚}},{√{𝑑}}) où 𝑚=2 ou un premier 𝑝≡1(𝑚𝑜𝑑4)
• LE 2-RANG DU GROUPE DE CLASSES DE CERTAINS CORPS BIQUADRATIQUES ET APPLICATIONS
• A genus theory for quartic fields.
• Pure quartic number fields whose class numbers are even.

This page was built for publication: The 2-rank of the real pure quartic number field \(K= \mathbb{Q}(\sqrt[4]{pd^{2}})\)