Let \(K/F\) be a finite field extension, and let \(\Aut(K/F)\) be the group of field automorphisms of \(K\) that restrict to the identity on \(F\). \(K/F\) is Galois if \(\abs{\Aut(K/F)} = [K: F]\).
In terms of $\abs{\Aut(K/F)}$, when is a finite extension $K/F$ Galois?