On Hilbert-Speiser type imaginary quadratic fields
Humio Ichimura, Hiroki Sumida-Takahashi (2009)
Acta Arithmetica
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Displaying similar documents to “Quadratic fields with infinite Hilbert 2-class field towers”
On Hilbert-Speiser type imaginary quadratic fields
Infinite Hilbert 2-class field tower of quadratic number fields
A. Mouhib (2010)
Acta Arithmetica
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Generalized Hilbert fields.
Kazimierz Szymiczek (1981)
Journal für die reine und angewandte Mathematik
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On preordered fields related to Hilbert's 17th problem.
Zeng Guangxin (1991)
Mathematische Zeitschrift
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Elements of order 4 of the Hilbert kernel in quadratic number fields
Qin Yue (2001)
Acta Arithmetica
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Imaginary quadratic fields satisfying the Hilbert-Speiser type condition for a small prime p
Humio Ichimura, Hiroki Sumida-Takahashi (2007)
Acta Arithmetica
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Infinite 2-class field towers of some imaginary quadratic number fields
Yutaka Sueyoshi (2004)
Acta Arithmetica
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On totally real Hilbert-Speiser fields of type Cₚ
Cornelius Greither, Henri Johnston (2009)
Acta Arithmetica
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An elementary proof of Komlós-Révész theorem in Hilbert spaces.
Guessous, Mohamed (1997)
Journal of Convex Analysis
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Hilbert-symbol equivalence of global function fields
Alfred Czogała (2001)
Mathematica Slovaca
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On the Hilbert -class field tower of some abelian -extensions over the field of rational numbers
Abdelmalek Azizi, Ali Mouhib (2013)
Czechoslovak Mathematical Journal
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It is well known by results of Golod and Shafarevich that the Hilbert -class field tower of any real quadratic number field, in which the discriminant is not a sum of two squares and divisible by eight primes, is infinite. The aim of this article is to extend this result to any real abelian -extension over the field of rational numbers. So using genus theory, units of biquadratic number fields and norm residue symbol, we prove that for every real abelian -extension over in which...