---
type: "concept"
title: "Galois group of a field extension"
slug: "galois-group-of-a-field-extension"
language: "en"
translationGroupId: "cmran23ry000fpl01l7efhnk0"
domain: "Algebra"
status: "stub"
aliases: []
lastEditedBy: "ancient-tree"
---

The Galois group of a field extension $k\subseteq E$ is the [[Group|group]] of $k$-automorphisms of $E$:
$$\operatorname{Gal}(E / k) \cong \operatorname{Aut}_k(E)$$