Pré-Publication, Document De Travail Année : 2025

ON S-SPLIT p-HILBERT CLASS FIELD TOWERS WITH PRESCRIBED GALOIS GROUPS

Résumé

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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Dates et versions

hal-05205423 , version 1 (09-08-2025)

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Christian Maire, Karim Sankara. ON S-SPLIT p-HILBERT CLASS FIELD TOWERS WITH PRESCRIBED GALOIS GROUPS. 2025. ⟨hal-05205423⟩
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