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The non-normal quartic CM-fields and the octic dihedral CM-fields with relative class number two. (English) Zbl 0976.11051
S. Louboutin and R. Okazaki have determined exactly all 38 non-isomorphic, non-normal quartic CM-fields with relative class number one and exactly all 19 non-isomorphic octic dihedral CM-fields with relative class number one [Acta Arith. 67, 47-62 (1994; Zbl 0809.11069)].
In this paper, the author intends to obtain analogous results for relative class number two and determines exactly all 254 non-isomorphic, non-normal quartic CM-fields with relative class number two and exactly all 95 non-isomorphic octic dihedral CM-fields with relative class number two. Moreover, by using this fact he determines precisely all 16 non-isomorphic octic dihedral CM-fields the ideal class groups of which the are nontrivial cyclic of 2-power order.

11R29 Class numbers, class groups, discriminants
11R21 Other number fields
Full Text: DOI
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