Theorems · Theorem · field theory
IsGalois.card_fixingSubgroup_eq_finrank
∀ {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] [IsGalois F E], Nat.card ↥K.fixingSubgroup = Module.finrank (↥K) E- Defined in
- Mathlib.FieldTheory.Galois.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 158 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.
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Subgroupstatement · cited by 3,593
- FiniteDimensionalstatement and proof · cited by 1,854
- Module.finrankstatement and proof · cited by 1,770
- AlgEquivstatement and proof · cited by 1,681
- IntermediateFieldstatement and proof · cited by 988
- Nat.cardstatement and proof · cited by 844
- IsGaloisstatement and proof · cited by 149
- IntermediateField.fixingSubgroupstatement and proof · cited by 41
- IntermediateField.finrank_fixedField_eq_cardproof · cited by 3
- IsGalois.fixedField_fixingSubgroupproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- IntermediateField.finrank_eq_fixingSubgroup_indexproof · cited by 1