Masses, discriminants, and Galois groups of tame quartic and quintic extensions of local fields (Q2901916)
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scientific article; zbMATH DE number 6062413
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Masses, discriminants, and Galois groups of tame quartic and quintic extensions of local fields |
scientific article; zbMATH DE number 6062413 |
Statements
31 July 2012
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\(p\)-adic
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Galois group
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local field
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quadratic
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quintic
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Masses, discriminants, and Galois groups of tame quartic and quintic extensions of local fields (English)
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Let \(K\) be a finite extension of the \(p\)-adic numbers with \(p\neq 2, 5\), and \(L/K\) a ramified extension. The author counted the number of non-isomorphic extensions where the Galois group of the splitting field of \(L\) is equal to one of the ten transitive subgroups of \(S_4\) and \(S_5\).
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