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arXiv · 2004.08899

Unit groups of some multiquadratic number fields and $2$-class groups

Mohamed Mahmoud Chems-Eddin
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Abstract

Let $p\equiv -q \equiv 5\pmod 8$ be two prime integers. In this paper, we investigate the unit groups of the fields $ L_1 =\mathbb{Q}(\sqrt 2, \sqrt{p}, \sqrt{q}, \sqrt{-1} )$ and $ L_1^+=\mathbb{Q}(\sqrt 2, \sqrt{p}, \sqrt{q} )$. Furthermore , we give the second $ 2$-class groups of the subextensions of $L_1$ as well the $2$-class groups of the fields $ L_n =\mathbb{Q}( \sqrt{p}, \sqrt{q}, ζ_{2^{n+2}} )$ and their maximal real subfelds.

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BibTeXRIS

Mohamed Mahmoud Chems-Eddin. 2020-09-25. Unit groups of some multiquadratic number fields and $2$-class groups. https://doi.org/10.1007/s10998-021-00402-0

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