Definition:Galois Extension/Finite/Definition 1

Definition

Let $L / K$ be a finite field extension.

$L / K$ is a (finite) Galois extension if and only if the fixed field of its automorphism group is $K$:

$\map {\operatorname{Fix}_L} {\Gal {L / K} } = K$

Also see

• Equivalence of Definitions of Finite Galois Extension

• Results about finite Galois extensions can be found here.

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