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A remark on the capitulation problem

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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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Acknowledgments

The author thanks the anonymous referee for his/her careful reading of the manuscript and helpful comments.

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Correspondence to Ali Mouhib.

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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

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