Definition:Galois Extension/Finite/Definition 1

Definition

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

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

$\map {\operatorname{Fix}_L} {\Gal {L / K} } = K$

Also see

• Equivalence of Definitions of Finite Galois Extension