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 $\Aut {L / K}$ equals the degree $\index L K$:

$\order {\Aut {L / K} } = \index L K$


Also see


Sources