Theorems · Theorem · group theory
AddSubgroup.map_equiv_normalizer_eq
∀ {G : Type u_1} [inst : AddGroup G] {N : Type u_5} [inst_1 : AddGroup N] (H : AddSubgroup G) (f : G ≃+ N),
AddSubgroup.map f.toAddMonoidHom (AddSubgroup.normalizer ↑H) =
AddSubgroup.normalizer ↑(AddSubgroup.map f.toAddMonoidHom 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 22 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddEquivstatement and proof · cited by 1,087
- map_addproof · cited by 964
- AddEquiv.symmproof · cited by 530
- map_negproof · cited by 378
- AddSubgroup.mapstatement · cited by 189
- AddEquiv.toEquivproof · cited by 174
- AddEquiv.toAddMonoidHomstatement · cited by 101
- AddSubgroup.extproof · cited by 75
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.map_normalizer_eq_of_bijectiveproof · cited by 0