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

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.