Abstract
It is well known from the results of Ferrero and Kida [2,7] that the \({\mathbb Z}_2\)-torsion part of the unramified abelian Iwasawa module \(X_{\infty}\) of any imaginary quadratic number field is trivial or cyclic of order 2. We will determine an infinite family of CM number fields, in which the \({\mathbb Z}_2\)-torsion of the Iwasawa module \(X_{\infty}\) is of arbitrary large rank, giving also the exact value of the rank of \(X_{\infty}\).
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The author is grateful to the anonymous referee for careful reading of the manuscript and for valuable comments and suggestions for the improvement of this article.
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Mouhib, A. The \(\mathbb{Z}_2\)-torsion of the cyclotomic \(\mathbb{Z}_2\)-extension of some CM number fields. Acta Math. Hungar. 170, 608–615 (2023). https://doi.org/10.1007/s10474-023-01359-x
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DOI: https://doi.org/10.1007/s10474-023-01359-x