The class number one problem for some non-abelian normal CM-fields
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- by Stéphane Louboutin, Ryotaro Okazaki and Michel Olivier PDF
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Abstract:
Let $\textbf {N}$ be a non-abelian normal CM-field of degree $4p,$ $p$ any odd prime. Note that the Galois group of $\textbf {N}$ is either the dicyclic group of order $4p,$ or the dihedral group of order $4p.$ We prove that the (relative) class number of a dicyclic CM-field of degree $4p$ is always greater then one. Then, we determine all the dihedral CM-fields of degree $12$ with class number one: there are exactly nine such CM-fields.References
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Additional Information
- Stéphane Louboutin
- Affiliation: Université de Caen, UFR Sciences, Département de Mathématiques, Esplanade de la paix, 14032 Caen Cedex, France
- Email: loubouti@math.unicaen.fr
- Ryotaro Okazaki
- Affiliation: Doshisha University, Department of Mathematics, Tanabe, Kyoto, 610-03, Japan
- Email: rokazaki@doshisha.ac.jp
- Michel Olivier
- Affiliation: Laboratoire A2X, UMR 99 36, Université Bordeaux I, 351 Cours de la Libération, 33405 Talence Cedex, France
- Email: olivier@math.u-bordeaux.fr
- Received by editor(s): July 16, 1995
- Received by editor(s) in revised form: March 21, 1996
- © Copyright 1997 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 349 (1997), 3657-3678
- MSC (1991): Primary 11R29; Secondary 11R21, 11R42, 11M20, 11Y40
- DOI: https://doi.org/10.1090/S0002-9947-97-01768-6
- MathSciNet review: 1390044