$2$-class groups of cyclotomic towers of imaginary biquadratic fields and applications

Mohamed Mahmoud Chems-Eddin; Katharina Müller

doi:10.1142/S1793042121500627

$2$-class groups of cyclotomic towers of imaginary biquadratic fields and applications

Number Theory 2021-03-10 v4

Authors: Mohamed Mahmoud Chems-Eddin , Katharina Müller

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Abstract

Let $d$ be a positive square-free integer. In this paper we shall investigate the structure of the $2$ -class group of the cyclotomic $\mathbb{Z}_2$ -extension of the imaginary biquadratic number field $\mathbb{Q}(\sqrt{d},\sqrt{-1})$ . Furthermore, we deduce the structure of the $2$ -class group of cyclotomic $\mathbb{Z}_2$ -extension of $\mathbb{Q}(\sqrt{-d})$ .

Keywords

2-class group cyclotomic z2-extension imaginary biquadratic field square-free integer number field

Cite

@article{arxiv.2002.03602,
  title  = {$2$-class groups of cyclotomic towers of imaginary biquadratic fields and applications},
  author = {Mohamed Mahmoud Chems-Eddin and Katharina Müller},
  journal= {arXiv preprint arXiv:2002.03602},
  year   = {2021}
}

Comments

We corrected some typos. 13 pages

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