Definition:Galois Extension/Finite/Definition 3

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

$L / K$ is a Galois extension the order of the automorphism group $\Aut {L / K}$ equals the degree $\index L K$:
 * $\order {\Aut {L / K} } = \index L K$

Also see

 * Equivalence of Definitions of Finite Galois Extension