Geodesic
Real quadratic number fields with metacyclic Hilbert $2$-class field tower
Mathematica Bohemica, Tome 144 (2019) no. 2, pp. 177-190

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

We begin by giving a criterion for a number field $K$ with 2-class group of rank 2 to have a metacyclic Hilbert 2-class field tower, and then we will determine all real quadratic number fields $\mathbb Q(\sqrt d)$ that have a metacyclic nonabelian Hilbert $2$-class field tower.
DOI : 10.21136/MB.2018.0102-17
Classification : 11R11, 11R29, 11R37
Keywords: class field tower; class group; real quadratic number field; metacyclic group 
@article{10_21136_MB_2018_0102_17,
     author = {Essahel, Said and Dakkak, Ahmed and Mouhib, Ali},
     title = {Real quadratic number fields with metacyclic {Hilbert} $2$-class field tower},
     journal = {Mathematica Bohemica},
     pages = {177--190},
     publisher = {mathdoc},
     volume = {144},
     number = {2},
     year = {2019},
     doi = {10.21136/MB.2018.0102-17},
     mrnumber = {3974186},
     zbl = {07088844},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2018.0102-17/}
}
TY  - JOUR
AU  - Essahel, Said
AU  - Dakkak, Ahmed
AU  - Mouhib, Ali
TI  - Real quadratic number fields with metacyclic Hilbert $2$-class field tower
JO  - Mathematica Bohemica
PY  - 2019
SP  - 177
EP  - 190
VL  - 144
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2018.0102-17/
DO  - 10.21136/MB.2018.0102-17
LA  - en
ID  - 10_21136_MB_2018_0102_17
ER  - 
%0 Journal Article
%A Essahel, Said
%A Dakkak, Ahmed
%A Mouhib, Ali
%T Real quadratic number fields with metacyclic Hilbert $2$-class field tower
%J Mathematica Bohemica
%D 2019
%P 177-190
%V 144
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2018.0102-17/
%R 10.21136/MB.2018.0102-17
%G en
%F 10_21136_MB_2018_0102_17
Essahel, Said; Dakkak, Ahmed; Mouhib, Ali. Real quadratic number fields with metacyclic Hilbert $2$-class field tower. Mathematica Bohemica, Tome 144 (2019) no. 2, pp. 177-190. doi: 10.21136/MB.2018.0102-17

Cité par Sources :