On the Hilbert $2$-class field towers of some cyclotomic $\mathbb{Z}_2$-extensions

Mohamed Mahmoud Chems-Eddin; Abdelkader Zekhnini; Abdelmalek Azizi

doi:10.1007/978-3-031-51959-8_2

On the Hilbert $2$-class field towers of some cyclotomic $\mathbb{Z}_2$-extensions

Number Theory 2024-05-30 v2

Authors: Mohamed Mahmoud Chems-Eddin , Abdelkader Zekhnini , Abdelmalek Azizi

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Abstract

In this paper, we study the length of the $2$ -class field towers and the structure of the Galois groups $\mathrm{Gal}(\mathcal{L}(K_n)/K_n)$ of the maximal unramified $2$ -extensions of the layers $K_n$ of the cyclotomic $\mathbb{Z}_2$ -extension of some special Dirichlet fields. The capitulation problem is investigated too.

Keywords

hilbert 2-class field tower cyclotomic z2-extension dirichlet field galois group capitulation problem unramified 2-extension

Cite

@article{arxiv.2005.06646,
  title  = {On the Hilbert $2$-class field towers of some cyclotomic $\mathbb{Z}_2$-extensions},
  author = {Mohamed Mahmoud Chems-Eddin and Abdelkader Zekhnini and Abdelmalek Azizi},
  journal= {arXiv preprint arXiv:2005.06646},
  year   = {2024}
}

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15 pages

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