Remark on infinite unramified extensions of number fields with class number one (Q1048930)
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scientific article; zbMATH DE number 5654996
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Remark on infinite unramified extensions of number fields with class number one |
scientific article; zbMATH DE number 5654996 |
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Remark on infinite unramified extensions of number fields with class number one (English)
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8 January 2010
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\textit{C. Maire} [On infinite unramified extensions, Pac. J. Math. 192, No. 1, 135--142 (2000; Zbl 1037.11074)] constructed some examples of biquadratic number fields, with trivial class group (and so, by class field theory, with no unramified abelian extensions) and an infinite unramified Galois extension. In this short paper the author modifies Maire's method to obtain other such examples, but with considerably smaller root discriminants.
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non-solvable unramified extensions
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biquadratic number fields
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