Theorems · Theorem · field theory

IsGaloisGroup.fixingSubgroup_fixedPoints

∀ (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] [Finite G],
  fixingSubgroup G ↑(FixedPoints.intermediateField ↥H) = H

Defined in

Mathlib.FieldTheory.Galois.IsGaloisGroup

Cited by

2 results in Mathlib

Foundations

Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupFieldFieldAlgebraMulSemiringActionIsGaloisGroupFinite