On the $2$-class group of some number fields with large degree

Chems-Eddin, Mohamed Mahmoud, Azizi, Abdelmalek, and Zekhnini, Abdelkader. "On the $2$-class group of some number fields with large degree." Archivum Mathematicum 057.1 (2021): 13-26. <http://eudml.org/doc/297322>.

@article{Chems2021,
abstract = {Let $d$ be an odd square-free integer, $m\ge 3$ any integer and $L_\{m, d\}:=\mathbb \{Q\}(\zeta _\{2^m\},\sqrt\{d\})$. In this paper, we shall determine all the fields $L_\{m, d\}$ having an odd class number. Furthermore, using the cyclotomic $\mathbb \{Z\}_2$-extensions of some number fields, we compute the rank of the $2$-class group of $L_\{m, d\}$ whenever the prime divisors of $d$ are congruent to $3$ or $5\hspace\{4.44443pt\}(\@mod \; 8)$.},
author = {Chems-Eddin, Mohamed Mahmoud, Azizi, Abdelmalek, Zekhnini, Abdelkader},
journal = {Archivum Mathematicum},
keywords = {cyclotomic $\mathbb \{Z\}_2$-extension; $2$-rank; $2$-class group},
language = {eng},
number = {1},
pages = {13-26},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On the $2$-class group of some number fields with large degree},
url = {http://eudml.org/doc/297322},
volume = {057},
year = {2021},
}

TY - JOUR
AU - Chems-Eddin, Mohamed Mahmoud
AU - Azizi, Abdelmalek
AU - Zekhnini, Abdelkader
TI - On the $2$-class group of some number fields with large degree
JO - Archivum Mathematicum
PY - 2021
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 057
IS - 1
SP - 13
EP - 26
AB - Let $d$ be an odd square-free integer, $m\ge 3$ any integer and $L_{m, d}:=\mathbb {Q}(\zeta _{2^m},\sqrt{d})$. In this paper, we shall determine all the fields $L_{m, d}$ having an odd class number. Furthermore, using the cyclotomic $\mathbb {Z}_2$-extensions of some number fields, we compute the rank of the $2$-class group of $L_{m, d}$ whenever the prime divisors of $d$ are congruent to $3$ or $5\hspace{4.44443pt}(\@mod \; 8)$.
LA - eng
KW - cyclotomic $\mathbb {Z}_2$-extension; $2$-rank; $2$-class group
UR - http://eudml.org/doc/297322
ER -