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Keywords:
unit group; multiquadratic number fields; unit index
unit group; multiquadratic number fields; unit index
Summary:
Let $p$ and $q$ be two different prime integers such that $p\equiv q\equiv 3\pmod 8$ with $(p/q)=1$, and $l$ a positive odd square-free integer relatively prime to $p$ and $q$. In this paper we investigate the unit groups of number fields $\mathbb L=\mathbb {Q}(\sqrt {2}, \sqrt {p}, \sqrt {q}, \sqrt {-l})$.
References:
[1] Azizi, A.: Unités de certains corps de nombres imaginaires et abéliens sur $\Bbb Q$. Ann. Sci. Math. Qué. 23 (1999), 15-21 French \99999MR99999 1721726 . MR 1721726 | Zbl 1041.11072
[2] Azizi, A., Chems-Eddin, M. M., Zekhnini, A.: Note on the Hilbert 2-class field tower. Math. Bohem. 147 (2022), 513-524 \99999DOI99999 10.21136/MB.2022.0056-21 . MR 4512171
[3] Chems-Eddin, M. M.: Arithmetic of some real triquadratic fields: Units and 2-class groups. Available at https://arxiv.org/abs/2108.04171v1 (2021), 32 pages.
[4] Chems-Eddin, M. M.: Unit groups of some multiquadratic number fields and 2-class groups. Period. Math. Hung. 84 (2022), 235-249. DOI 10.1007/s10998-021-00402-0 | MR 4423478 | Zbl 07551296
[5] Chems-Eddin, M. M.: On units of some fields of the form $\Bbb{Q}(\sqrt2, \sqrt{p}, \sqrt{q}, \sqrt{-\ell})$. Math. Bohem. 148 (2023), 237-242. DOI 10.21136/MB.2022.0128-21 | MR 4585579 | Zbl 7729575
[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. DOI 10.1007/s40590-021-00329-z | MR 4220815 | Zbl 1468.11223
[7] Chems-Eddin, M. M., Zekhnini, A., Azizi, A.: Units and 2-class field towers of some multiquadratic number fields. Turk. J. Math. 44 (2020), 1466-1483. DOI 10.3906/mat-2003-117 | MR 4122918 | Zbl 1455.11140
[8] Chems-Eddin, M. M., Zekhnini, A., Azizi, A.: On the Hilbert 2-class field towers of some cyclotomic $\Bbb Z_2$-extensions. Available at https://arxiv.org/abs/2005.06646 (2021), 15 pages.
[9] Chems-Eddin, M. M., Zekhnini, A., Azizi, A.: Unit groups of some multiquadratic number fields of degree 16. São Paulo J. Math. Sci 16 (2022), 1091-1096. DOI 10.1007/s40863-020-00209-w | MR 4515950 | Zbl 7626140
[10] Kubota, T.: Über den bizyklischen biquadratischen Zahlkörper. Nagoya Math. J. 10 (1956), 65-85 German. DOI 10.1017/S0027763000000088 | MR 0083009 | Zbl 0074.03001
[11] Wada, H.: On the class number and the unit group of certain algebraic number fields. J. Fac. Sci., Univ. Tokyo, Sect. I 13 (1966), 201-209. MR 0214565 | Zbl 0158.30103
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