On the 2-class field towers of some imaginary quartic cyclic number fields

DOI10.4064/CM7690-10-2018zbMath1454.11198OpenAlexW2962824174WikidataQ127458709 ScholiaQ127458709MaRDI QIDQ5237146

Abdelmalek Azizi, Mohammed Talbi, Idriss Jerrari, Abdelkader Zekhnini

Publication date: 16 October 2019

Published in: Colloquium Mathematicum (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4064/cm7690-10-2018

zbMATH Keywords

capitulationHilbert class field2-groups

Mathematics Subject Classification ID

Galois theory (11R32) Quadratic extensions (11R11) Class field theory (11R37) Cubic and quartic extensions (11R16) Class numbers, class groups, discriminants (11R29)

Cites Work

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• On the second 2-class group \(\mathrm{Gal}(K_2^{(2)} / K)\) of some imaginary quartic cyclic number field \(K\)
• Algebraic investigations of Hilbert's theorem 94, the principal ideal theorem and the capitulation problem
• Real quadratic fields with abelian 2-class field tower
• Divisibility by 8 of the class number of quadratic fields whose 2-class group is cyclic, and biquadratic reciprocity
• Sur les \(\ell\)-classes d'idéaux dans les extensions cycliques rélatives de degré premier \(\ell\). I
• Ideal class groups of cyclotomic number fields I

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