Theorems · Definition · field theory

IsGalois.normalAutEquivQuotient

{K : Type u_3} →
  {L : Type u_4} →
    [inst : Field K] →
      [inst_1 : Field L] →
        [inst_2 : Algebra K L] →
          [FiniteDimensional K L] →
            [IsGalois K L] →
              (H : Subgroup Gal(L/K)) → [inst_5 : H.Normal] → Gal(L/K) ⧸ H ≃* Gal(↥(IntermediateField.fixedField H)/K)

If H is a normal Subgroup of Gal(L / K), then Gal(fixedField H / K) is isomorphic to Gal(L / K) ⧸ H.

Defined in

Mathlib.FieldTheory.Galois.Basic

Cited by

1 results in Mathlib

Foundations

Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldFieldAlgebraFiniteDimensionalIsGaloisSubgroup.Normal