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December 2016 The Capitulation Problem for Certain Cyclic Quartic Number Fields
Abdelmalek AZIZI, Idriss JERRARI, Mohammed TALBI
Tokyo J. Math. 39(2): 351-359 (December 2016). DOI: 10.3836/tjm/1484903127

Abstract

Let $K$ be a cyclic quartic number field such that its 2-class group is of type $(2,4)$, $K_2^{(1)}$ be the Hilbert 2-class field of $K$, $K_2^{(2)}$ be the Hilbert 2-class field of $K_2^{(1)}$ and $G=\text{Gal}(K_2^{(2)}/K)$ be the Galois group of $K_2^{(2)}/K$. Our goal is to study the capitulation problem of 2-ideal classes of $K$ and to determine the structure of $G$.

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Abdelmalek AZIZI. Idriss JERRARI. Mohammed TALBI. "The Capitulation Problem for Certain Cyclic Quartic Number Fields." Tokyo J. Math. 39 (2) 351 - 359, December 2016. https://doi.org/10.3836/tjm/1484903127

Information

Published: December 2016
First available in Project Euclid: 20 January 2017

zbMATH: 1381.11104
MathSciNet: MR3599497
Digital Object Identifier: 10.3836/tjm/1484903127

Subjects:
Primary: 11R27
Secondary: 11R37

Rights: Copyright © 2016 Publication Committee for the Tokyo Journal of Mathematics

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Vol.39 • No. 2 • December 2016
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