Class numbers of real cyclic number fields with small conductor
John Myron Masley (1978)
Compositio Mathematica
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Displaying similar documents to “A survey of computational class field theory”
Class numbers of real cyclic number fields with small conductor
The class number one problem for some non-abelian normal CM-fields of degree
F. Lemmermeyer, S. Louboutin, R. Okazaki (1999)
Journal de théorie des nombres de Bordeaux
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We determine all the non-abelian normal CM-fields of degree 24 with class number one, provided that the Galois group of their maximal real subfields is isomorphic to , the alternating group of degree and order . There are two such fields with Galois group (see Theorem 14) and at most one with Galois group SL (see Theorem 18); if the generalized Riemann hypothesis is true, then this last field has class number .
Some unsolved problems
W. Narkiewicz (1971)
Mémoires de la Société Mathématique de France
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Stickelberger elements in function fields
David R. Hayes (1985)
Compositio Mathematica
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CM-fields with all roots of unity
Kuniaki Horie (1990)
Compositio Mathematica
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On -categorical theories of fields
Angus Macintyre (1971)
Fundamenta Mathematicae
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Ten problems on quadratic forms
Kazimierz Szymiczek (2002)
Acta Mathematica et Informatica Universitatis Ostraviensis
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The imaginary abelian number fields with class numbers equal to their genus class numbers
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.