Czechoslovak Mathematical Journal

Czechoslovak Mathematical Journal, Vol. 72, No. 4, pp. 1145-1156, 2022

On the structure of the 2-Iwasawa module of some number fields of degree 16

Idriss Jerrari, Abdelmalek Azizi

Received October 22, 2021. Published online April 26, 2022.

Abstract: 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 $K$.

Keywords: cyclic quartic field; cyclotomic $\mathbb Z_2$-extension; 2-Iwasawa module; 2-class group; 2-rank

Classification MSC: 11R16, 11R18, 11R20, 11R23, 11R29

DOI: 10.21136/CMJ.2022.0398-21

PDF available at: Springer Institute of Mathematics CAS Digital Mathematics Library

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Affiliations: Idriss Jerrari (corresponding author), Abdelmalek Azizi, Mohammed First University, Department of Mathematics, Faculty of Sciences, Mohammed V avenue, P.O.Box 524, Oujda 60000, Morocco, e-mail: idriss_math@hotmail.fr, abdelmalekazizi@yahoo.fr

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