Theorems · Theorem · field theory

IsGaloisGroup.fixedPoints_fixingSubgroup

∀ (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] (F : IntermediateField K L) [hGKL : IsGaloisGroup G K L]
  [Finite G], FixedPoints.intermediateField ↥(fixingSubgroup G ↑F) = F

Defined in: Mathlib.FieldTheory.Galois.IsGaloisGroup
Cited by: 0 results in Mathlib
Foundations: Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Group Field Field Algebra MulSemiringAction IsGaloisGroup Finite

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Algebrastatement and proof · cited by 11,388
SetLike.coestatement · cited by 8,199
Fieldstatement and proof · cited by 7,404
Groupstatement and proof · cited by 6,238
Subgroupstatement and proof · cited by 3,593
Finitestatement and proof · cited by 3,029
IntermediateFieldstatement and proof · cited by 988
MulSemiringActionstatement and proof · cited by 423
IsGaloisGroupstatement and proof · cited by 96
fixingSubgroupstatement · cited by 83
OrderIso.symm_apply_applyproof · cited by 41
FixedPoints.intermediateFieldstatement and proof · cited by 18

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