Theorems · Theorem · field theory
IsGalois.fixedField_fixingSubgroup
∀ {F : Type u_1} [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E] (K : IntermediateField F E)
[FiniteDimensional F E] [h : IsGalois F E], IntermediateField.fixedField K.fixingSubgroup = KSee InfiniteGalois.fixedField_fixingSubgroup for the infinite case,
i.e. without the [FiniteDimensional F E] assumption.
- Defined in
- Mathlib.FieldTheory.Galois.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- FiniteDimensionalstatement and proof · cited by 1,854
- Module.finrankproof · cited by 1,770
- le_rflproof · cited by 1,558
- IntermediateFieldstatement and proof · cited by 988
- IsGaloisstatement and proof · cited by 149
- Nat.card_congrproof · cited by 133
- MulEquiv.toEquivproof · cited by 126
- IntermediateField.fixingSubgroupstatement and proof · cited by 41
- IntermediateField.fixedFieldstatement and proof · cited by 25
- IsGalois.card_aut_eq_finrankproof · cited by 16
Cited by3
Results whose statement or proof uses this declaration.
- IsGalois.intermediateFieldEquivSubgroupproof · cited by 10
- IsGalois.fixedField_topproof · cited by 2
- IsGalois.card_fixingSubgroup_eq_finrankproof · cited by 1