On some imaginary triquadratic number fields k with Cl 2 ( k ) ≃ ( 2 , 4 ) or ( 2 , 2 , 2 )

Abdelmalek Azizi; Mohamed Mahmoud Chems-Eddin; Abdelkader Zekhnini

Commentationes Mathematicae Universitatis Carolinae (2021)

  • Issue: 1, page 1-14
  • ISSN: 0010-2628

Abstract

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Let d be a square free integer and L d : = ℚ ( ζ 8 , d ) . In the present work we determine all the fields L d such that the 2 -class group, Cl 2 ( L d ) , of L d is of type ( 2 , 4 ) or ( 2 , 2 , 2 ) .

How to cite

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Azizi, Abdelmalek, Chems-Eddin, Mohamed Mahmoud, and Zekhnini, Abdelkader. "On some imaginary triquadratic number fields $k$ with ${\rm Cl}_2(k) \simeq (2, 4)$ or $(2, 2, 2)$." Commentationes Mathematicae Universitatis Carolinae (2021): 1-14. <http://eudml.org/doc/298193>.

@article{Azizi2021,
abstract = {Let $d$ be a square free integer and $L_d:=\mathbb \{Q\}(\zeta _\{8\},\sqrt\{d\})$. In the present work we determine all the fields $L_d$ such that the $2$-class group, $\mathrm \{Cl\}_2(L_d)$, of $L_d$ is of type $(2,4)$ or $(2,2,2)$.},
author = {Azizi, Abdelmalek, Chems-Eddin, Mohamed Mahmoud, Zekhnini, Abdelkader},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$2$-group rank; $2$-class group; imaginary triquadratic number fields},
language = {eng},
number = {1},
pages = {1-14},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On some imaginary triquadratic number fields $k$ with $\{\rm Cl\}_2(k) \simeq (2, 4)$ or $(2, 2, 2)$},
url = {http://eudml.org/doc/298193},
year = {2021},
}

TY - JOUR
AU - Azizi, Abdelmalek
AU - Chems-Eddin, Mohamed Mahmoud
AU - Zekhnini, Abdelkader
TI - On some imaginary triquadratic number fields $k$ with ${\rm Cl}_2(k) \simeq (2, 4)$ or $(2, 2, 2)$
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2021
PB - Charles University in Prague, Faculty of Mathematics and Physics
IS - 1
SP - 1
EP - 14
AB - Let $d$ be a square free integer and $L_d:=\mathbb {Q}(\zeta _{8},\sqrt{d})$. In the present work we determine all the fields $L_d$ such that the $2$-class group, $\mathrm {Cl}_2(L_d)$, of $L_d$ is of type $(2,4)$ or $(2,2,2)$.
LA - eng
KW - $2$-group rank; $2$-class group; imaginary triquadratic number fields
UR - http://eudml.org/doc/298193
ER -

References

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