Finite-field Frobenius automorphism
= Finite-field Frobenius automorphism
{title2=$x\mapsto x^q$}
The map $x\mapsto x^q$ is an automorphism of $\mathbb F_{q^n}$ fixing $\mathbb F_q$. Its powers are all the $\mathbb F_q$-automorphisms, and its order is $n$.