On alternating and symmetric groups as Galois groups (Q1881735)
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scientific article; zbMATH DE number 2108113
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On alternating and symmetric groups as Galois groups |
scientific article; zbMATH DE number 2108113 |
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On alternating and symmetric groups as Galois groups (English)
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15 October 2004
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The main result of the paper under review states that the alternating group \(A_n,n\geq 3\) appears as Galois group over any Hilbertian fi eld of characteristic \(\neq 2\). In characteristic 2 the same statement holds for odd \(n\). The proof uses Newton polygons. It is further shown, that any quadratic extension of Hilbertian fields of characteristic different from 2 can be embedded in an \(S_n\)-extension.
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Galois extension
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Hilbertian fields
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alternating group
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symmetric group
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Newton polygon
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