---
tag: 0Q5NA8Y362
kind: concept
name: Galois group of a polynomial
msc: [12F10]
sources:
  - url: https://en.wikipedia.org/wiki/Galois_group
    locator: Galois group of a polynomial
---

## Summary

The Galois group of a polynomial over a field is the Galois group of its splitting field.
It acts on the roots of the polynomial by permutations.
The [[definition of the Galois group of a polynomial|0JZY3R908H]] states it.