Theorems · Definition · field theory
IntermediateField.fixingSubgroup
{F : Type u_1} →
[inst : Field F] →
{E : Type u_2} → [inst_1 : Field E] → [inst_2 : Algebra F E] → IntermediateField F E → Subgroup Gal(E/F)The subgroup fixing an intermediate field.
- Defined in
- Mathlib.FieldTheory.Galois.Basic
- Cited by
- 41 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- SetLike.coeproof · cited by 8,199
- Fieldstatement and proof · cited by 7,404
- Subgroupstatement · cited by 3,593
- AlgEquivstatement and proof · cited by 1,681
- IntermediateFieldstatement and proof · cited by 988
- fixingSubgroupproof · cited by 83
Cited by49
Results whose statement or proof uses this declaration.
- IsGalois.intermediateFieldEquivSubgroupproof · cited by 10
- IntermediateField.le_iff_lestatement and proof · cited by 5
- fixedByFiniteproof · cited by 5
- IntermediateField.fixingSubgroup_isOpenstatement and proof · cited by 5
- IntermediateField.fixingSubgroup_botstatement · cited by 4
- IsGalois.intermediateFieldEquivSubgroup_applystatement · cited by 3
- IntermediateField.fixingSubgroupEquivstatement and proof · cited by 3
- IntermediateField.fixingSubgroup_fixedFieldstatement and proof · cited by 3
- IntermediateField.fixingSubgroup_lestatement and proof · cited by 3
- InfiniteGalois.fixedField_fixingSubgroupstatement and proof · cited by 3
- IsGalois.fixedField_fixingSubgroupstatement and proof · cited by 2
- IntermediateField.fixingSubgroup_antitonestatement · cited by 2