Theorems · Theorem · field theory
FiniteGaloisIntermediateField.mem_fixingSubgroup_iff
∀ {k : Type u_1} {K : Type u_2} [inst : Field k] [inst_1 : Field K] [inst_2 : Algebra k K] (α : Gal(K/k))
(L : FiniteGaloisIntermediateField k K),
α ∈ L.fixingSubgroup ↔ (AlgEquiv.restrictNormalHom ↥L.toIntermediateField) α = 1- Defined in
- Mathlib.FieldTheory.Galois.GaloisClosure
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- MonoidHomstatement · cited by 3,629
- Subgroupstatement · cited by 3,593
- AlgEquivstatement and proof · cited by 1,681
- IntermediateFieldstatement · cited by 988
- IntermediateField.fixingSubgroupstatement · cited by 41
- FiniteGaloisIntermediateFieldstatement and proof · cited by 32
- FiniteGaloisIntermediateField.toIntermediateFieldstatement and proof · cited by 25
- AlgEquiv.restrictNormalHomstatement · cited by 21
- AlgEquiv.restrictNormalHom_applyproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- InfiniteGalois.isOpen_mulEquivToLimit_image_fixingSubgroupproof · cited by 1