On s-split p-Hilbert class field towers with prescribed Galois groups

Christian Maire; Karim Sankara

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arXiv · 2508.07946

On s-split p-Hilbert class field towers with prescribed Galois groups

Christian Maire·Karim Sankara

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Abstract

In this work, we show that given a finite p-group G, a number field K having a trivial p-class group Cl K , and a finite set of primes S of K, there exists a finite extension F/K such that the S-split p-Hilbert class field tower L S p (F ) of F has G as its Galois group. This extends results by Ozaki and Hajir-Maire-Ramakrishna.

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Christian Maire, Karim Sankara. 2025-08-11. On s-split p-Hilbert class field towers with prescribed Galois groups. https://arxiv.org/abs/2508.07946

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