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arXiv · 1911.11198

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

Mohamed Mahmoud Chems-Eddin·Abdelmalek Azizi·Abdelkader Zekhnini
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Abstract

Let $d$ be an odd square-free integer, $m\geq 3$ any integer and $L_{m, d}:=\mathbb{Q}(\zeta_{2^m},\sqrt{d})$. In this paper, we shall determine all the fields $L_{m, d}$ having an odd class number. Furthermore, using the cyclotomic $\mathbb{Z}_2$-extensions of some number fields, we compute the rank of the $2$-class group of $L_{m, d}$ whenever the prime divisors of $d$ are congruent to $3$ or $5\pmod 8$.

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Mohamed Mahmoud Chems-Eddin, Abdelmalek Azizi, Abdelkader Zekhnini. 2019-11-25. On the $2$-class group of some number fields with large degree. https://doi.org/10.5817/am2021-1-13

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