---
tag: 0XTY86BZKY
kind: concept
name: Galois group
msc: [12F10]
sources:
  - url: https://en.wikipedia.org/wiki/Galois_group
    locator: lead section
same_as:
  wikidata: Q730384
  wikipedia: Galois group
---

## Summary

The Galois group of a field extension $L/K$ is the group of the automorphisms of $L$ that fix every element of $K$.
The [[definition of the Galois group|0XVR72M51M]] gives the details.