For a field F with prime characteristic p, the Frobenius endomorphism is the map φ‎: F→F defined by φ‎(r) = r^p. Note φ‎ is clearly multiplicative and is additive as the binomial coefficient $\left(\begin{array}{c}p\\ k\end{array}\right)$ is divisible by p for 0<k<p. By Fermat’s Little Theorem, φ‎ fixes the prime subfield. If F is finite, then φ‎ is an automorphism and generates the Galois group of F over the prime subfield.