The non-abelian normal CM-fields of degree 36 with class number one
Ku-Young Chang, Soun-Hi Kwon (2002)
Acta Arithmetica
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Ku-Young Chang, Soun-Hi Kwon (2002)
Acta Arithmetica
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Stéphane R. Louboutin (2006)
Acta Arithmetica
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Bernhard Schmidt (2005)
Acta Arithmetica
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Kâzim Ilhan Ikeda, Erol Serbest (2010)
Acta Arithmetica
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Henri Johnston (2006)
Acta Arithmetica
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Ku-Young Chang, Soun-Hi Kwon (2000)
Journal de théorie des nombres de Bordeaux
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We know that there exist only finitely many imaginary abelian number fields with class numbers equal to their genus class numbers. Such non-quadratic cyclic number fields are completely determined in [Lou2,4] and [CK]. In this paper we determine all non-cyclic abelian number fields with class numbers equal to their genus class numbers, thus the one class in each genus problem is solved, except for the imaginary quadratic number fields.
Keiji Okano (2006)
Acta Arithmetica
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Radan Kučera (2002)
Acta Mathematica et Informatica Universitatis Ostraviensis
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Mikihito Hirabayashi, Ken-ichi Yoshino (1989)
Manuscripta mathematica
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Manabu Ozaki, Hisao Taya (1995)
Manuscripta mathematica
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Louboutin, Stéphane (1998)
Experimental Mathematics
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Fernando Fernández Rodríguez, Agustín Llerena Achutegui (1991)
Extracta Mathematicae
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We say that a field K has the Extension Property if every automorphism of K(X) extends to an automorphism of K. J.M. Gamboa and T. Recio [2] have introduced this concept, naive in appearance, because of its crucial role in the study of homogeneity conditions in spaces of orderings of functions fields. Gamboa [1] has studied several classes of fields with this property: Algebraic extensions of the field Q of rational numbers; euclidean, algebraically closed and pythagorean fields; fields...
K. Ramachandra (1969)
Journal für die reine und angewandte Mathematik
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Stéphane Louboutin (1996)
Manuscripta mathematica
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