Geodesic
On the $2$-class group of some number fields with large degree
Archivum mathematicum, Tome 57 (2021) no. 1, pp. 13-26

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 $5\pmod 8$.
DOI : 10.5817/AM2021-1-13
Classification : 11R11, 11R23, 11R29, 11R32
Keywords: cyclotomic $\mathbb{Z}_2$-extension; $2$-rank; $2$-class group 
@article{10_5817_AM2021_1_13,
     author = {Chems-Eddin, Mohamed Mahmoud and Azizi, Abdelmalek and Zekhnini, Abdelkader},
     title = {On the $2$-class group of some number fields with large degree},
     journal = {Archivum mathematicum},
     pages = {13--26},
     publisher = {mathdoc},
     volume = {57},
     number = {1},
     year = {2021},
     doi = {10.5817/AM2021-1-13},
     mrnumber = {4260837},
     zbl = {07332701},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5817/AM2021-1-13/}
}
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
SP  - 13
EP  - 26
VL  - 57
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.5817/AM2021-1-13/
DO  - 10.5817/AM2021-1-13
LA  - en
ID  - 10_5817_AM2021_1_13
ER  - 
%0 Journal Article
%A Chems-Eddin, Mohamed Mahmoud
%A Azizi, Abdelmalek
%A Zekhnini, Abdelkader
%T On the $2$-class group of some number fields with large degree
%J Archivum mathematicum
%D 2021
%P 13-26
%V 57
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.5817/AM2021-1-13/
%R 10.5817/AM2021-1-13
%G en
%F 10_5817_AM2021_1_13
Chems-Eddin, Mohamed Mahmoud; Azizi, Abdelmalek; Zekhnini, Abdelkader. On the $2$-class group of some number fields with large degree. Archivum mathematicum, Tome 57 (2021) no. 1, pp. 13-26. doi: 10.5817/AM2021-1-13

Cité par Sources :