On embedding problems with restricted ramifications. (Q1125392)
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scientific article; zbMATH DE number 1375099
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On embedding problems with restricted ramifications. |
scientific article; zbMATH DE number 1375099 |
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On embedding problems with restricted ramifications. (English)
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1999
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Let \(L/k\) be a finite Galois extension of algebraic number fields, with Galois group \(G\), and let \( 1\to A\to E\to G\to 1\) be a central extension of groups. The author investigates the existence of the Galois extension \(M/L/k\) such that the Galois group \(\mathrm{Gal}(M/k)\) is isomorphic to \(E\) and that \(M/L\) is unramified outside a finite set of primes of \(L\). The class number of the Hilbert \(p\)-class field is also discussed.
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Galois extension
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algebraic number fields
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central extension of groups
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unramified extension
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class numbers
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