Theorems · Theorem · group theory
AddSubgroup.map_normalizer_eq_of_bijective
∀ {G : Type u_1} [inst : AddGroup G] {N : Type u_5} [inst_1 : AddGroup N] (H : AddSubgroup G) {f : G →+ N},
Function.Bijective ⇑f → AddSubgroup.map f (AddSubgroup.normalizer ↑H) = AddSubgroup.normalizer ↑(AddSubgroup.map f H)The image of the normalizer is equal to the normalizer of the image of a bijective function.
- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- SetLike.coestatement · cited by 8,199
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddMonoidHomstatement and proof · cited by 3,230
- Function.Bijectivestatement and proof · cited by 863
- AddSubgroup.mapstatement · cited by 189
- AddSubgroup.normalizerstatement · cited by 59
- AddEquiv.ofBijectiveproof · cited by 5
- AddSubgroup.map_equiv_normalizer_eqproof · cited by 1
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.