Definition:Galois Extension/Finite/Definition 1

Definition
Let $L/K$ be a finite field extension.

$L/K$ is a Galois extension the fixed field of its automorphism group is $K$:


 * $\operatorname{Fix}_L(\operatorname{Gal}(L/K)) = K$

Also see

 * Equivalence of Definitions of Finite Galois Extension