Article
| Title: | On the structure of the 2-Iwasawa module of some number fields of degree 16 (English) |
| Author: | Jerrari, Idriss |
| Author: | Azizi, Abdelmalek |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 72 |
| Issue: | 4 |
| Year: | 2022 |
| Pages: | 1145-1156 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Let $K$ be an imaginary cyclic quartic number field whose 2-class group is of type $(2, 2, 2)$, i.e., isomorphic to $\mathbb {Z}/2\mathbb {Z}\times \mathbb {Z}/2\mathbb {Z}\times \mathbb {Z}/2\mathbb {Z}$. The aim of this paper is to determine the structure of the Iwasawa module of the genus field $K^{(*)}$ of $K$. (English) |
| Keyword: | cyclic quartic field |
| Keyword: | cyclotomic $\mathbb Z_2$-extension |
| Keyword: | 2-Iwasawa module |
| Keyword: | 2-class group |
| Keyword: | 2-rank |
| MSC: | 11R16 |
| MSC: | 11R18 |
| MSC: | 11R20 |
| MSC: | 11R23 |
| MSC: | 11R29 |
| idZBL: | Zbl 07655789 |
| idMR: | MR4517602 |
| DOI: | 10.21136/CMJ.2022.0398-21 |
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| Date available: | 2022-11-28T11:41:00Z |
| Last updated: | 2023-04-11 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151136 |
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| Reference: | [1] Azizi, A., Jerrari, I., Zekhnini, A., Talbi, M.: On the second 2-class group $ Gal(K_2^{(2)}/K)$ of some imaginary quartic cyclic number field $K$.J. Number Theory 177 (2017), 562-588. Zbl 1428.11190, MR 3629256, 10.1016/j.jnt.2017.01.027 |
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| Reference: | [3] Chems-Eddin, M. M.: The 2-Iwasawa module over certain octic elementary fields.Available at https://arxiv.org/abs/2007.05953 (2020), 4 pages. |
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| Reference: | [9] Kida, Y.: Cyclotomic $Z_2$-extensions of $J$-fields.J. Number Theory 14 (1982), 340-352. Zbl 0493.12015, MR 0660379, 10.1016/0022-314X(82)90069-5 |
| Reference: | [10] Lemmermeyer, F.: Reciprocity Laws: From Euler to Eisenstein.Springer Monographs in Mathematics. Springer, Berlin (2000). Zbl 0949.11002, MR 1761696, 10.1007/978-3-662-12893-0 |
| Reference: | [11] Müller, K.: Capitulation in the cyclotomic $Z_2$ extension of CM number fields.Math. Proc. Camb. Philos. Soc. 166 (2019), 371-380. Zbl 1462.11099, MR 3903123, 10.1017/S0305004118000026 |
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