Real quadratic number fields with metacyclic Hilbert -class field tower
Said Essahel; Ahmed Dakkak; Ali Mouhib
Mathematica Bohemica (2019)
- Volume: 144, Issue: 2, page 177-190
- ISSN: 0862-7959
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topEssahel, Said, Dakkak, Ahmed, and Mouhib, Ali. "Real quadratic number fields with metacyclic Hilbert $2$-class field tower." Mathematica Bohemica 144.2 (2019): 177-190. <http://eudml.org/doc/294501>.
@article{Essahel2019,
abstract = {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.},
author = {Essahel, Said, Dakkak, Ahmed, Mouhib, Ali},
journal = {Mathematica Bohemica},
keywords = {class field tower; class group; real quadratic number field; metacyclic group},
language = {eng},
number = {2},
pages = {177-190},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Real quadratic number fields with metacyclic Hilbert $2$-class field tower},
url = {http://eudml.org/doc/294501},
volume = {144},
year = {2019},
}
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
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 144
IS - 2
SP - 177
EP - 190
AB - 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.
LA - eng
KW - class field tower; class group; real quadratic number field; metacyclic group
UR - http://eudml.org/doc/294501
ER -
References
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