Abstract
For the cyclotomic \({\mathbb Z_2}\)-extension k ∞ of an imaginary quadratic field k, we consider whether the Galois group G(k ∞) of the maximal unramified pro-2-extension over k ∞ is abelian or not. The group G(k ∞) is abelian if and only if the nth layer of the \({\mathbb {Z}_2}\)-extension has abelian 2-class field tower for all n ≥ 1. The purpose of this paper is to classify all such imaginary quadratic fields k in part by using Iwasawa polynomials.
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Mizusawa, Y., Ozaki, M. Abelian 2-class field towers over the cyclotomic \({\mathbb {Z}_2}\)-extensions of imaginary quadratic fields. Math. Ann. 347, 437–453 (2010). https://doi.org/10.1007/s00208-009-0431-8
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DOI: https://doi.org/10.1007/s00208-009-0431-8