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

Authors

IDRISS JERRARI
ABDELMALEK AZIZI

DOI

10.55730/1300-0098.3287

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

First Page

2545

Last Page

2555

Recommended Citation

JERRARI, IDRISS and AZIZI, ABDELMALEK (2022) "On the $2$-class group of some number fields of $2$-power degree," Turkish Journal of Mathematics: Vol. 46: No. 7, Article 1. https://doi.org/10.55730/1300-0098.3287
Available at: https://journals.tubitak.gov.tr/math/vol46/iss7/1