Work demonstrates existence of extensions with specific Galois groups in number fields with trivial class groups.
In this work, we show that given a finite [Formula: see text]-group [Formula: see text], a number field [Formula: see text] having a trivial [Formula: see text]-class group [Formula: see text], and a finite set of primes [Formula: see text] of [Formula: see text], there exists a finite extension [Formula: see text] such that the [Formula: see text]-split [Formula: see text]-Hilbert class field tower [Formula: see text] of [Formula: see text] has [Formula: see text] as its Galois group. This extends results by Ozaki and Hajir-Maire-Ramakrishna.
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Maire et al. (2026) studied this question.
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