\begin{definition}[Definition:Galois Extension/Finite/Definition 3]
Let $L / K$ be a finite field extension
$L / K$ is a '''Galois extension''' {{iff}} the order of the automorphism group $\Aut {L / K}$ equals the degree $\index L K$:
:$\order {\Aut {L / K} } = \index L K$
\end{definition}