Abstract
For an imaginary biquadratic number field \(L = \mathbb{Q}(i,\sqrt{d})\), where d is an odd square-free integer, let \(L_\infty\) be the cyclotomic \(\mathbb{Z}_2\)-extension of L. For any integer \(n \geq 0\), we denote by Ln the nth layer of \(L_{\infty}/L\). We study the rank of the 2-primary part of the class group of Ln and then we draw the list of all number fields L where the Galois group of the maximal unramified pro-2-extension of \(L_\infty\) is metacyclic.
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28 February 2024
A Correction to this paper has been published: https://doi.org/10.1007/s10474-024-01404-3
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The authors are grateful to the anonymous referee for careful reading of the manuscript, valuable comments and suggestions.
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Mouhib, A., Rouas, S. On the rank of the 2-class group of some imaginary biquadratic number fields. Acta Math. Hungar. 167, 295–308 (2022). https://doi.org/10.1007/s10474-022-01224-3
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DOI: https://doi.org/10.1007/s10474-022-01224-3