On the strongly ambiguous classes of some biquadratic number fields

Title:

On the strongly ambiguous classes of some biquadratic number fields

Creator:

Azizi, Abdelmalek, Zekhnini, Abdelkader, and Taous, Mohammed

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:b3c7bb74-f3ac-4ddd-ba7b-ed7f7b3bfa59
uuid:b3c7bb74-f3ac-4ddd-ba7b-ed7f7b3bfa59
doi:10.21136/MB.2016.0022-14

Subject:

absolute genus field, relative genus field, fundamental system of units, 2-class group, capitulation, quadratic field, biquadratic field, and multiquadratic CM-field

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We study the capitulation of 2-ideal classes of an infinite family of imaginary bicyclic biquadratic number fields consisting of fields k = Q( √ 2pq, i), where i = √ −1 and p ≡ −q ≡ 1 (mod 4) are different primes. For each of the three quadratic extensions K/k inside the absolute genus field k (∗) of k, we determine a fundamental system of units and then compute the capitulation kernel of K/k. The generators of the groups Ams(k/F) and Am(k/F) are also determined from which we deduce that k (∗) is smaller than the relative genus field (k/Q(i))∗ . Then we prove that each strongly ambiguous class of k/Q(i) capitulates already in k (∗) , which gives an example generalizing a theorem of Furuya (1977).

Language:

English

Rights:

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

Coverage:

363-384

Source:

Mathematica bohemica | 2016 Volume:141 | Number:3

Harvested from:

CDK

Metadata only:

false