The $2$-rank of the class group of some real cyclic quartic number fields II

Authors: ABDELMALEK AZIZI, MOHAMMED TAMIMI, ABDELKADER ZEKHNINI

Abstract: In this paper, we determine the $2$-rank of the class group of certain classes of real cyclic quartic number fields. Precisely, we consider the case in which the quadratic subfield is $\mathbb{Q}(\sqrt{\ell})$ with $\ell=2$ or a prime congruent to $1\,\pmod8$.

Keywords: Real cyclic quartic number field, $2$-rank, $2$-class group, quadratic fields, quartic extensios

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