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The class number one problem for the dihedral and dicyclic CM-fields. (English) Zbl 1036.11056
The author describes results on dihedral and dicyclic CM-fields with relative class number one obtained by him and several coauthors [see, S. Louboutin and R. Okazaki, Proc. Lond. Math. Soc. (3) 76, 523–548 (1998; Zbl 0891.11054), and with M. Olivier, Trans. Am. Math. Soc. 349, 3657–3678 (1997; Zbl 0893.11045)], and uses these results to show that dicyclic CM-fields of degree \(4n\), \(n > 1\), have relative class number \(> 1\).

MSC:
11R29 Class numbers, class groups, discriminants
11R21 Other number fields
11Y40 Algebraic number theory computations
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