Weyl groups as Galois groups of a regular extension of the field \(\mathbb{Q}\) (Q1918782)
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scientific article; zbMATH DE number 907270
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Weyl groups as Galois groups of a regular extension of the field \(\mathbb{Q}\) |
scientific article; zbMATH DE number 907270 |
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Weyl groups as Galois groups of a regular extension of the field \(\mathbb{Q}\) (English)
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15 October 1997
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It is proved that all Weyl groups except those of type \(F_4\) are realized as Galois groups of a regular extension of the rational function field \(\mathbb{Q} (T)\). The author uses a uniform method to find a rigid rational triplet for each Weyl group (except those of types \(D_{2k}\) and \(F_4\)) and the results of \textit{G. V. Belyi} [Izv. Akad. Nauk SSSR, Ser. Mat. 43, 267-276 (1979; Zbl 0409.12012)]. Remark that the Weyl group of type \(F_4\), excluded from the main theorem, is solvable.
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Weyl groups
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Galois groups
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regular extension
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rational function fields
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rigid rational triplet
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0.89399284
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0.85805416
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0.85601074
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0.85486174
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