On the Hilbert $2$-class field tower of some abelian $2$-extensions over the field of rational numbers

Title:

On the Hilbert $2$-class field tower of some abelian $2$-extensions over the field of rational numbers

Creator:

Azizi, Abdelmalek and Mouhib, Ali

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:69afcf2e-48ca-4653-bb4e-c9745a804373
uuid:69afcf2e-48ca-4653-bb4e-c9745a804373

Subject:

class group, class field tower, and multiquadratic number field

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

It is well known by results of Golod and Shafarevich that the Hilbert $2$-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 $2$-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 $2$-extension over $\mathbb Q$ in which eight primes ramify and one of theses primes $\equiv -1\pmod 4$, the Hilbert $2$-class field tower is infinite.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

1135-1148

Source:

Czechoslovak Mathematical Journal | 2013 Volume:63 | Number:4

Harvested from:

CDK

Metadata only:

false