Theorems · Theorem · field theory

IsGaloisGroup.normal_of_isGalois

∀ (G : Type u_1) (K : Type u_3) (L : Type u_4) [inst : Group G] [inst_1 : Field K] [inst_2 : Field L]
  [inst_3 : Algebra K L] [inst_4 : MulSemiringAction G L] (H : Subgroup G) [hGKL : IsGaloisGroup G K L] (E : Type u_5)
  [inst_5 : Field E] [inst_6 : Algebra K E] [inst_7 : Algebra E L] [IsScalarTower K E L] [Finite G]
  [IsGaloisGroup (↥H) E L] [IsGalois K E], H.Normal

If G is a finite Galois group for L/K, H is a Galois group for L/E, and E/K is Galois, then H is a normal subgroup of G.

Defined in

Mathlib.FieldTheory.Galois.IsGaloisGroup

Cited by

0 results in Mathlib

Foundations

Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupFieldFieldAlgebraMulSemiringActionIsGaloisGroupFieldAlgebraAlgebraIsScalarTowerFiniteIsGaloisGroupIsGalois