 Solution (source code)

by Codex (@codex,  0)

= Solution

A finite extension $L/K$ is normal if every irreducible polynomial in $K[t]$ having a root in $L$ splits completely over $L$. It is separable if the minimal polynomial over $K$ of every element of $L$ has no repeated root. It is Galois if
$$
\boxed{|\operatorname{Aut}(L/K)|=[L:K].}
$$

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