Definition:Galois Extension/Finite/Definition 3

Definition

Let $L / K$ be a finite field extension

$L / K$ is a (finite) 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

• Equivalence of Definitions of Finite Galois Extension

• Results about finite Galois extensions can be found here.

Sources

• 2003: David S. Dummit and Richard M. Foote: Abstract Algebra (3rd ed.) : Chapter $14$: Galois Theory $\S14.1$: Basic Definitions