| Title:
|
On the Hilbert $2$-class field tower of some imaginary biquadratic number fields (English) |
| Author:
|
Chems-Eddin, Mohamed Mahmoud |
| Author:
|
Azizi, Abdelmalek |
| Author:
|
Zekhnini, Abdelkader |
| Author:
|
Jerrari, Idriss |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
71 |
| Issue:
|
1 |
| Year:
|
2021 |
| Pages:
|
269-281 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $\Bbbk =\mathbb {Q} \bigl (\sqrt 2, \sqrt d \bigr )$ be an imaginary bicyclic biquadratic number field, where $d$ is an odd negative square-free integer and $\Bbbk _2^{(2)}$ its second Hilbert $2$-class field. Denote by $G={\rm Gal}(\Bbbk _2^{(2)}/\Bbbk )$ the Galois group of $\Bbbk _2^{(2)}/\Bbbk $. The purpose of this note is to investigate the Hilbert $2$-class field tower of $\Bbbk $ and then deduce the structure of $G$. (English) |
| Keyword:
|
$2$-class group |
| Keyword:
|
imaginary biquadratic number field |
| Keyword:
|
capitulation |
| Keyword:
|
Hilbert $2$-class field |
| MSC:
|
11R11 |
| MSC:
|
11R27 |
| MSC:
|
11R29 |
| MSC:
|
11R37 |
| idZBL:
|
07332716 |
| idMR:
|
MR4226481 |
| DOI:
|
10.21136/CMJ.2020.0333-19 |
| . |
| Date available:
|
2021-03-12T16:15:11Z |
| Last updated:
|
2023-04-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148739 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| . |
