### References & Citations

# Mathematics > Number Theory

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

(Submitted on 10 Feb 2020 (v1), last revised 7 Jan 2021 (this version, v4))

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 $\mathbb{Q}(\sqrt{-d})$.

## Submission history

From: Mohamed Mahmoud Chems-Eddin [view email]**[v1]**Mon, 10 Feb 2020 08:38:41 GMT (11kb)

**[v2]**Tue, 11 Feb 2020 14:18:33 GMT (11kb)

**[v3]**Mon, 15 Jun 2020 20:19:25 GMT (13kb)

**[v4]**Thu, 7 Jan 2021 10:17:02 GMT (14kb)

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