Necessary condition and sufficient for certain Galois group to be metacyclic

DOI10.5802/AMBP.255zbMath1168.11046OpenAlexW2507038307MaRDI QIDQ1017366

Abdelmalek Azizi, Mohammed Taous

Publication date: 18 May 2009

Published in: Annales Mathématiques Blaise Pascal (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AMBP_2009__16_1_83_0

zbMATH Keywords

Galois groupclass field towerHilbert class fieldmetacyclic extensions

Mathematics Subject Classification ID

Units and factorization (11R27) Class field theory (11R37) Class numbers, class groups, discriminants (11R29)

Related Items (1)

On the rank of the 2-class group of \(\mathbb Q(\sqrt{p},\sqrt{q},\sqrt{-1})\)

Cites Work

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• On a special class of \(p\)-groups
• Number fields with class number congruent to 4 mod 8 and Hilbert's Theorem 94
• Real quadratic fields with abelian 2-class field tower
• Imaginary quadratic fields \(k\) with cyclic \(\text{Cl}_2(k^1)\)
• Imaginary bicyclic biquadratic fields with cyclic 2-class group
• 2-groups of almost maximal class
• Sur une question de capitulation
• Über die Beziehung der Klassenzahlen der Unterkörper des bizyklischen bizuadratischen Zahlkörpers
• Imaginary quadratic fields \(k\) with \(\text{Cl}_ 2(k)\simeq(2,2^ m)\) and rank \(\text{Cl}_ 2(k^ 1)=2\).

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