\begin{definition}[Definition:Galois Extension/Finite/Definition 1]
Let $L/K$ be a finite field extension.
$L/K$ is a '''Galois extension''' {{Iff}} the fixed field of its automorphism group is $K$:
:$\map {\operatorname{Fix}_L} {\Gal {L / K} } = K$
\end{definition}