✦ LIBER ✦
The Non-normal Quartic CM-Fields and the Octic Dihedral CM-Fields with Relative Class Number Two
✍ Scribed by Hee-Sun Yang; Soun-Hi Kwon
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 157 KB
- Volume
- 79
- Category
- Article
- ISSN
- 0022-314X
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✦ Synopsis
In this paper we determine all non-normal quartic CM-fields with relative class number two and all octic dihedral CM-fields with relative class number two: there are exactly 254 non-isomorphic non-normal quartic CM-fields with relative class number two and 95 non-isomorphic octic dihedral CM-fields with relative class number two. This result permits us to find all octic dihedral CM-fields of which ideal class groups are nontrivial and cyclic of 2-power order: there are precisely 16 non-isomorphic such octic dihedral CM-fields.