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arXiv · 1503.03530

On the strongly ambiguous classes of $k/Q(\sqrt{-1})$ where $k= Q(\sqrt{2p_1p_2},\sqrt{-1})$

Abdelmalek Azizi·Abdelkader Zekhnini·Mohammed Taous
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Abstract

We construct an infinite family of imaginary bicyclic biquadratic number fields $k$ with the 2-ranks of their 2-class groups are $\geq3$, whose strongly ambiguous classes of $k/Q(i)$ capitulate in the absolute genus field $k^{(*)}$, which is strictly included in the relative genus field $(k/Q(i))^*$ and we study the capitulation of the $2$-ideal classes of $k$ in its quadratic extensions included in $k^{(*)}$.

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Abdelmalek Azizi, Abdelkader Zekhnini, Mohammed Taous. 2015-03-11. On the strongly ambiguous classes of $k/Q(\sqrt{-1})$ where $k= Q(\sqrt{2p_1p_2},\sqrt{-1})$. https://doi.org/10.1142/s1793557114500211

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