Definition:Galois Extension/Finite/Definition 3

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Definition

Let $L / K$ be a finite field extension


$L / K$ is a Galois extension if and only if 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


Sources