On the $2$-class group of some number fields of $2$-power degree

Authors: IDRISS JERRARI, ABDELMALEK AZIZI

Abstract: Let $K$ be an imaginary cyclic quartic number field whose $2$-class group is isomorphic to $\mathbb{Z}/2\mathbb{Z}\times\mathbb{Z}/2\mathbb{Z}$, and let $K^*$ denote the genus field of $K$. In this paper, we compute the rank of the $2$-class group of $K^*_n$ the $n$-th layer of the cyclotomic $Z_2$-extension of $K^*$.

Keywords: Iwasawa theory, cyclotomic $Z_2$-extension, cyclic quartic field, $2$-class group

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