# Infinite class field towers of number fields of prime power discriminant

## TL;DR

This paper proves that for every prime p, there exists a solvable number field with ramification only at p and infinity, whose p-Hilbert Class field tower is infinite, advancing understanding of class field towers.

## Contribution

It demonstrates the existence of infinite class field towers for specific solvable number fields ramified only at a prime p and infinity.

## Key findings

- Existence of such number fields for all primes p.
- Infinite p-Hilbert Class field towers established.
- Solvability of the fields involved.

## Abstract

For every prime number p, we show the existence of a solvable number field L ramified only at {p and infinity whose p-Hilbert Class field tower is infinite.