Azizi, A. and Zekhnini, A. and Taous, M. (2016) On the strongly ambiguous classes of some biquadratic number fields. Mathematica Bohemica, 141 (3). pp. 363-384.

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Abstract

We study the capitulation of 2-ideal classes of an infinite family of imaginary bicyclic biquadratic number fields consisting of fields (formula presented), where (formula presented) 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). © 2016, Akademie ved Ceske Republiky. All rights reserved.

Item Type: Article
Subjects: Mathematics
Divisions: SCIENTIFIC PRODUCTION > Mathematics
Depositing User: Administrateur Eprints Administrateur Eprints
Last Modified: 31 Jan 2020 15:48
URI: http://eprints.umi.ac.ma/id/eprint/4014

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