| Title:
|
Note on the Hilbert 2-class field tower (English) |
| Author:
|
Azizi, Abdelmalek |
| Author:
|
Chems-Eddin, Mohamed Mahmoud |
| Author:
|
Zekhnini, Abdelkader |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
147 |
| Issue:
|
4 |
| Year:
|
2022 |
| Pages:
|
513-524 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $k$ be a number field with a 2-class group isomorphic to the Klein four-group. The aim of this paper is to give a characterization of capitulation types using group properties. Furthermore, as applications, we determine the structure of the second 2-class groups of some special Dirichlet fields $\Bbbk =\Bbb {Q}\big (\sqrt d, \sqrt {-1}\big )$, which leads to a correction of some parts in the main results of A. Azizi and A. Zekhini (2020). (English) |
| Keyword:
|
multiquadratic field |
| Keyword:
|
fundamental systems of units |
| Keyword:
|
2-class group |
| Keyword:
|
2-class field tower |
| Keyword:
|
capitulation |
| MSC:
|
11R11 |
| MSC:
|
11R16 |
| MSC:
|
11R20 |
| MSC:
|
11R27 |
| MSC:
|
11R29 |
| MSC:
|
11R37 |
| idZBL:
|
Zbl 07655824 |
| idMR:
|
MR4512171 |
| DOI:
|
10.21136/MB.2022.0056-21 |
| . |
| Date available:
|
2022-11-16T11:17:53Z |
| Last updated:
|
2023-04-11 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151096 |
| . |
| Reference:
|
[1] Azizi, A.: Sur le 2-groupe de classes d'idéaux de $\mathbb Q(\sqrt d, i)$.Rend. Circ. Mat. Palermo, II. Ser. French 48 (1999), 71-92. Zbl 0920.11076, MR 1705171, 10.1007/BF02844380 |
| Reference:
|
[2] Azizi, A.: Unités de certains corps de nombres imaginaires et abéliens sur $\mathbb Q$.Ann. Sci. Math. Qué. 23 (1999), 15-21 French. Zbl 1041.11072, MR 1721726 |
| Reference:
|
[3] Azizi, A., Benhamza, I.: Sur la capitulation des 2-classes d'idéaux de $\mathbb Q(\sqrt d, \sqrt{-2})$.Ann. Sci. Math. Qué. French 29 (2005), 1-20. Zbl 1217.11097, MR 2296826 |
| Reference:
|
[4] Azizi, A., Zekhnini, A.: The structure of the second 2-class group of some special Dirichlet fields.Asian-Eur. J. Math. 13 (2020), Article ID 2050053, 6 pages. Zbl 1442.11154, MR 4096421, 10.1142/S1793557120500539 |
| Reference:
|
[5] Azizi, A., Zekhnini, A., Taous, M.: The generators of the 2-class group of some field $\mathbb Q(\sqrt{pq_1q_2,i})$: Correction to Theorem 3 of [5].Int. J. Pure Appl. Math. 103 (2015), 99-107. MR 3405725, 10.12732/ijpam.v103i1.8 |
| Reference:
|
[6] Chems-Eddin, M. M., Azizi, A., Zekhnini, A.: Unit groups and Iwasawa lambda invariants of some multiquadratic number fields.Bol. Soc. Mat. Mex., III. Ser. 27 (2021), Article ID 24, 16 pages. Zbl 07342807, MR 4220815, 10.1007/s40590-021-00329-z |
| 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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| . |
