---
type: "concept"
title: "Galois group of a polynomial"
slug: "galois-group-of-a-polynomial"
language: "en"
translationGroupId: "cmran7ivg000lpl0149soqe60"
domain: "Algebra"
status: "stub"
aliases: []
lastEditedBy: "ancient-tree"
---

The Galois group of a [[Polynomial|polynomial]] $P$ of $K[X]$ is the [[Galois group of a field extension|Galois group]] of a [[Splitting field|splitting field]] $K\subseteq E$ of $P$:
$$\operatorname{Gal}_K(P)=\operatorname{Gal}(E/K)$$