Geodesic
On the structure of the 2-Iwasawa module of some number fields of degree 16
Czechoslovak Mathematical Journal, Tome 72 (2022) no. 4, pp. 1145-1156
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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 $K$.
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 $K$.
DOI : 10.21136/CMJ.2022.0398-21
Classification : 11R16, 11R18, 11R20, 11R23, 11R29
Keywords: cyclic quartic field; cyclotomic $\mathbb Z_2$-extension; 2-Iwasawa module; 2-class group; 2-rank 
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Jerrari, Idriss; Azizi, Abdelmalek. On the structure of the 2-Iwasawa module of some number fields of degree 16. Czechoslovak Mathematical Journal, Tome 72 (2022) no. 4, pp. 1145-1156. doi: 10.21136/CMJ.2022.0398-21

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