The non-abelian normal CM-fields of degree 36 with class number one (Q2773318)
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scientific article; zbMATH DE number 1709910
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The non-abelian normal CM-fields of degree 36 with class number one |
scientific article; zbMATH DE number 1709910 |
Statements
The non-abelian normal CM-fields of degree 36 with class number one (English)
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21 February 2002
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CM-field
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relative class number
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class field theory
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class numbers
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class groups
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minus class number
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The authors pursue the classification of all normal CM-fields of class number one, a family proved to be finite by \textit{A. M. Odlyzko} [Invent. Math. 29, 275--286 (1975; Zbl 0299.12010)]. The fields under examination are non-abelian of degree \(4p^2\), \(p\) an odd prime, and all the candidates in this list are found. The proof uses a combination of algebraic arguments, numerical computations and the results of \textit{S. Louboutin, R. Okazaki} and \textit{M. Olivier} [Trans. Am. Math. Soc. 349, 3657--3678 (1997; Zbl 0893.11045)] and of \textit{K.-Y. Chang} and \textit{S.-H. Kwon} [Proc. Am. Math. Soc. 128, 2517--2528 (2000; Zbl 0983.11064)]. As usual in these questions, the key point consists in reducing the field to be explored numerically by sufficiently strong theoretical arguments.
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