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.

## 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 &#x01d542;/&#x01d542; inside the absolute genus field &#x01d542;(*) of &#x01d542;, we determine a fundamental system of units and then compute the capitulation kernel of &#x01d542;/&#x01d542;. The generators of the groups Ams(&#x01d542;/F) and Am(&#x01d542;/F) are also determined from which we deduce that &#x01d542;(*) is smaller than the relative genus field (&#x01d542;/ℚ(i))*. Then we prove that each strongly ambiguous class of &#x01d542;/ℚ(i) capitulates already in &#x01d542;(*), which gives an example generalizing a theorem of Furuya (1977). © 2016, Akademie ved Ceske Republiky. All rights reserved.

Item Type: | Article |
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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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