Computing the Fixed Field of $\text{Aut}(\mathbb{F}(x)/\mathbb{F})$

Richard Mandel

For a finite field $\mathbb{F}$, it is a basic result of Galois theory that the fixed field $E$ of $\text{Aut}(\mathbb{F}(x)/\mathbb{F})$ is a proper extension of $\mathbb{F}$. In…