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 $\operatorname{Aut} \left({L / K}\right)$ equals the degree $\left[{L : K}\right]$:
 * $\left\vert{\operatorname{Aut} \left({L / K}\right)}\right\vert = \left[{L : K}\right]$

Also see

 * Equivalence of Definitions of Finite Galois Extension