On Imaginary abelian number fields of type (2, 2, ..., 2) with one class in each genus.

Ichiro Miyada

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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.