Theorems · Theorem · group theory
Subgroup.map_equiv_normalizer_eq
∀ {G : Type u_1} [inst : Group G] {N : Type u_5} [inst_1 : Group N] (H : Subgroup G) (f : G ≃* N),
Subgroup.map f.toMonoidHom (Subgroup.normalizer ↑H) = Subgroup.normalizer ↑(Subgroup.map f.toMonoidHom H)The image of the normalizer is equal to the normalizer of the image of an isomorphism.
- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- SetLike.coestatement · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- MulEquivstatement and proof · cited by 1,142
- map_mulproof · cited by 1,137
- MulEquiv.symmproof · cited by 482
- Subgroup.mapstatement · cited by 301
- MulEquiv.toEquivproof · cited by 126
- MulEquiv.toMonoidHomstatement · cited by 126
- Subgroup.extproof · cited by 108
- Subgroup.normalizerstatement · cited by 108
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.map_normalizer_eq_of_bijectiveproof · cited by 0