On S-Split p-Hilbert Class Field Towers with Prescribed Galois Groups

TL;DR

This paper demonstrates that for any finite p-group G, one can construct a number field extension with a prescribed Galois group for its S-split p-Hilbert class field tower, extending previous results.

Contribution

It establishes the existence of number field extensions with specified Galois groups for their S-split p-Hilbert class field towers, generalizing prior work.

Findings

Existence of extensions with prescribed Galois groups for S-split p-Hilbert class field towers.

Extension of previous results by Ozaki and Hajir-Maire-Ramakrishna.

Construction applicable for any finite p-group G and suitable base fields.

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.