# Automorphism groups over Hilbertian fields

## TL;DR

This paper proves that any finite group can be realized as the automorphism group of infinitely many finite extensions over any Hilbertian field, generalizing previous results from global fields.

## Contribution

It extends and unifies prior work by showing the universality of automorphism groups over Hilbertian fields for finite extensions.

## Key findings

- Every finite group occurs as an automorphism group over Hilbertian fields.
- Infinitely many such extensions exist for each finite group.
- Generalization of previous results from global fields.

## Abstract

We show that every finite group occurs as the automorphism group of infinitely many finite (field) extensions of any given Hilbertian field. This extends and unifies previous results of M. Fried and Takahashi on the global field case.