On the strongly ambiguous classes of some biquadratic number fields

2015/03/06 by Abdelmalek Azizi, Azizi, Abdelmalek, Abdelkader Zekhnini +3 · 1 citation
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1503.01992

arxiv created 2015/03/06 · arxiv updated 2015/03/09

Abstract

We study the capitulation of ideal classes in an infinite family of imaginary bicyclic biquadratic number fields consisting of fields k =Q(√(2pq), i), where i=√(-1) and p≡ -q≡1 \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 (k/Q(i))^*.

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• Capitulation in the absolutely abelian extensions of some fields ℚ(√(p₁p₂q), √(-1))

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