The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
Soient des nombres premiers distincts , et . On peut approcher le -rang du groupe de classes des corps en étudiant celui du corps pour un entier . Dans cet article, on traite le cas où ou . Comme application, on déduit que le rang du -groupe de classes de est au moins égal à deux (on savait déjà grâce à un résultat de Fröhlich que le groupe de classes de est toujours d’ordre pair). On en déduit également la liste de tous les corps multiquadratiques ayant un -groupe de classes...
It is well known by results of Golod and Shafarevich that the Hilbert -class field tower of any real quadratic number field, in which the discriminant is not a sum of two squares and divisible by eight primes, is infinite. The aim of this article is to extend this result to any real abelian -extension over the field of rational numbers. So using genus theory, units of biquadratic number fields and norm residue symbol, we prove that for every real abelian -extension over in which eight primes...
Let be a biquadratic field, be the Hilbert -class field of and be the Hilbert -class field of . Our goal is to prove that there exists a biquadratic field such that and the group is semi-dihedral. Résumé. Soient un corps biquadratique, le -corps de classes de Hilbert de et le -corps de classes de Hilbert de . Notre but est de prouver qu’il existe des corps biquadratiques réels tels que le groupe est de type et le groupe est semi-diédral.
We begin by giving a criterion for a number field 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 that have a metacyclic nonabelian Hilbert -class field tower.
Download Results (CSV)