---
tag: 0CGCPX8Z70
kind: concept
name: Frobenius automorphism of a finite field
msc: ["12E20"]
sources:
  - url: https://en.wikipedia.org/wiki/Finite_field
    locator: Frobenius automorphism and Galois theory
---

## Summary

The Frobenius automorphism of a finite field of characteristic $p$ is the map $x \mapsto x^p$.
It generates the group of all automorphisms of the field.
The [[definition of the Frobenius automorphism|0VP4TBVJ19]] gives the details.