For a Galois extension field K of a field F, the fundamental theorem of Galois theory states that the subgroups of the Galois group G = Gal(K/F) correspond with the subfields of K containing F. If the subfield L corresponds to the subgroup H, then the extension field degree of K over L is the group order of H, left bracketing bar K:L right bracketing bar | = | left bracketing bar H right bracketing bar left bracketing bar L:F right bracketing bar | = | left bracketing bar G:H right bracketing bar .

field automorphism | Galois theory