Definition:Fixed Field

Definition
Let $F$ be a field.

Let $G \leq \operatorname{Aut}(F)$ be a subgroup of the group of automorphisms of $F$.

The fixed field of $G$ is the set:
 * $\operatorname{Fix}(G) = \{f\in F : \forall \sigma \in G : \sigma(f) = f\}$

Also denoted as
The fixed field of $G$ can also be denoted $F_G$ or $\operatorname{Fix}_F(G)$ to emphasize that it is contained in $F$.

Also see

 * Fixed Field is Field