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Ku-Young Chang; Soun-Hi Kwon
The imaginary abelian number fields with class numbers equal to their genus class numbers
Journal de théorie des nombres de Bordeaux, 12 no. 2 (2000), p. 349-365, doi: 10.5802/jtnb.283
Article PDF | Reviews MR 1823189 | Zbl 0972.11107

Résumé - Abstract

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.

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