On the Hilbert 2 -class field tower of some imaginary biquadratic number fields

Mohamed Mahmoud Chems-Eddin; Abdelmalek Azizi; Abdelkader Zekhnini; Idriss Jerrari

Czechoslovak Mathematical Journal (2021)

  • Issue: 1, page 269-281
  • ISSN: 0011-4642

Abstract

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Let 𝕜 = ℚ 2 , d be an imaginary bicyclic biquadratic number field, where d is an odd negative square-free integer and 𝕜 2 ( 2 ) its second Hilbert 2 -class field. Denote by G = Gal ( 𝕜 2 ( 2 ) / 𝕜 ) the Galois group of 𝕜 2 ( 2 ) / 𝕜 . The purpose of this note is to investigate the Hilbert 2 -class field tower of 𝕜 and then deduce the structure of G .

How to cite

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Chems-Eddin, Mohamed Mahmoud, et al. "On the Hilbert $2$-class field tower of some imaginary biquadratic number fields." Czechoslovak Mathematical Journal (2021): 269-281. <http://eudml.org/doc/296964>.

@article{Chems2021,
abstract = {Let $\mathbb \{k\}=\mathbb \{Q\} \bigl (\sqrt\{2\}, \sqrt\{d\} \bigr )$ be an imaginary bicyclic biquadratic number field, where $d$ is an odd negative square-free integer and $\mathbb \{k\}_2^\{(2)\}$ its second Hilbert $2$-class field. Denote by $G=\{\rm Gal\}(\mathbb \{k\}_2^\{(2)\}/\mathbb \{k\})$ the Galois group of $\mathbb \{k\}_2^\{(2)\}/\mathbb \{k\}$. The purpose of this note is to investigate the Hilbert $2$-class field tower of $\mathbb \{k\}$ and then deduce the structure of $G$.},
author = {Chems-Eddin, Mohamed Mahmoud, Azizi, Abdelmalek, Zekhnini, Abdelkader, Jerrari, Idriss},
journal = {Czechoslovak Mathematical Journal},
keywords = {$2$-class group; imaginary biquadratic number field; capitulation; Hilbert $2$-class field},
language = {eng},
number = {1},
pages = {269-281},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the Hilbert $2$-class field tower of some imaginary biquadratic number fields},
url = {http://eudml.org/doc/296964},
year = {2021},
}

TY - JOUR
AU - Chems-Eddin, Mohamed Mahmoud
AU - Azizi, Abdelmalek
AU - Zekhnini, Abdelkader
AU - Jerrari, Idriss
TI - On the Hilbert $2$-class field tower of some imaginary biquadratic number fields
JO - Czechoslovak Mathematical Journal
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 269
EP - 281
AB - Let $\mathbb {k}=\mathbb {Q} \bigl (\sqrt{2}, \sqrt{d} \bigr )$ be an imaginary bicyclic biquadratic number field, where $d$ is an odd negative square-free integer and $\mathbb {k}_2^{(2)}$ its second Hilbert $2$-class field. Denote by $G={\rm Gal}(\mathbb {k}_2^{(2)}/\mathbb {k})$ the Galois group of $\mathbb {k}_2^{(2)}/\mathbb {k}$. The purpose of this note is to investigate the Hilbert $2$-class field tower of $\mathbb {k}$ and then deduce the structure of $G$.
LA - eng
KW - $2$-class group; imaginary biquadratic number field; capitulation; Hilbert $2$-class field
UR - http://eudml.org/doc/296964
ER -

References

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