no. 2
The imaginary abelian number fields with class numbers equal to their genus class numbers
Journal de théorie des nombres de Bordeaux, Tome 12 (2000) no. 2, pp. 349-365.

Titre français : Sur les corps abéliens dont le nombre de classes est égal au nombre de genres. Nous savons qu'il n'existe qu'un nombre fini de corps abéliens imaginaires pour lesquels le nombre de classes est égal au nombre de genres. Ceux de ces corps qui sont cycliques et non quadratiques ont été classés dans [Lou2,4] et dans [CK]. Dans cet article, nous déterminons tous les corps abéliens non cycliques dont le nombre de classes est égal au nombre de genres. Cela achève la classification des corps abéliens possédant une classe par genre, sauf dans le cas des corps quadratiques imaginaires.

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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     title = {The imaginary abelian number fields with class numbers equal to their genus class numbers},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {349--365},
     publisher = {Universit\'e Bordeaux I},
     volume = {12},
     number = {2},
     year = {2000},
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Chang, Ku-Young; Kwon, Soun-Hi. The imaginary abelian number fields with class numbers equal to their genus class numbers. Journal de théorie des nombres de Bordeaux, Tome 12 (2000) no. 2, pp. 349-365. http://archive.numdam.org/item/JTNB_2000__12_2_349_0/

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