Theorems · Theorem · group theory
MulEquiv.normal_map_iff
∀ {G : Type u_1} {G' : Type u_2} [inst : Group G] [inst_1 : Group G'] {f : G ≃* G'} {H : Subgroup G},
(Subgroup.map (↑f) H).Normal ↔ H.Normal- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 74 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.
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- MulEquivstatement and proof · cited by 1,142
- MulEquiv.symmproof · cited by 482
- Subgroup.Normalstatement and proof · cited by 334
- Subgroup.mapstatement · cited by 301
- MonoidHomClass.toMonoidHomstatement · cited by 294
- MulEquiv.surjectiveproof · cited by 41
- Subgroup.map_equiv_eq_comap_symmproof · cited by 6
- Subgroup.normal_comap_iff_of_surjectiveproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- IsGaloisGroup.normal_of_isGaloisproof · cited by 0