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arXiv · 1503.01992

On the strongly ambiguous classes of some biquadratic number fields

Abdelmalek Azizi·Abdelkader Zekhnini·Mohammed Taous
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Abstract

We study the capitulation of ideal classes in an infinite family of imaginary bicyclic biquadratic number fields consisting of fields $k =Q(\sqrt{2pq}, i)$, where $i=\sqrt{-1}$ and $p\equiv -q\equiv1 \pmod 4$ are different primes. For each of the three quadratic extensions $K/k$ inside the absolute genus field $k^{(*)}$ of $k$, we compute the capitulation kernel of $K/k$. Then we deduce that each strongly ambiguous class of $k/Q(i)$ capitulates already in $k^{(*)}$, which is smaller than the relative genus field $\left(k/Q(i)\right)^*$.

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Abdelmalek Azizi, Abdelkader Zekhnini, Mohammed Taous. 2015-03-06. On the strongly ambiguous classes of some biquadratic number fields. https://arxiv.org/abs/1503.01992

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