| Title:
|
On the $2$-class group of some number fields with large degree (English) |
| Author:
|
Chems-Eddin, Mohamed Mahmoud |
| Author:
|
Azizi, Abdelmalek |
| Author:
|
Zekhnini, Abdelkader |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
57 |
| Issue:
|
1 |
| Year:
|
2021 |
| Pages:
|
13-26 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $d$ be an odd square-free integer, $m\ge 3$ any integer and $L_{m, d}:=\mathbb{Q}(\zeta _{2^m},\sqrt{d})$. In this paper, we shall determine all the fields $L_{m, d}$ having an odd class number. Furthermore, using the cyclotomic $\mathbb{Z}_2$-extensions of some number fields, we compute the rank of the $2$-class group of $L_{m, d}$ whenever the prime divisors of $d$ are congruent to $3$ or $5\pmod 8$. (English) |
| Keyword:
|
cyclotomic $\mathbb{Z}_2$-extension |
| Keyword:
|
$2$-rank |
| Keyword:
|
$2$-class group |
| MSC:
|
11R11 |
| MSC:
|
11R23 |
| MSC:
|
11R29 |
| MSC:
|
11R32 |
| idZBL:
|
Zbl 07332701 |
| idMR:
|
MR4260837 |
| DOI:
|
10.5817/AM2021-1-13 |
| . |
| Date available:
|
2021-03-05T10:31:38Z |
| Last updated:
|
2021-11-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148715 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
