Abstract
We determine explicitly an infinite family of imaginary cyclic number fields k, such that the 2-class group of k is elementary with arbitrary large 2-rank and capitulates in an unramified quadratic extension K. The infinitely many number fields k and K have the same Hilbert 2-class field and an infinite Hilbert 2-class field tower.
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The author thanks the anonymous referee for his/her careful reading of the manuscript and helpful comments.
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Mouhib, A. A remark on the capitulation problem. Period Math Hung 73, 120–129 (2016). https://doi.org/10.1007/s10998-016-0144-1
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DOI: https://doi.org/10.1007/s10998-016-0144-1