Theorems · Theorem · group theory
AddSubgroup.characteristic_iff_le_comap
∀ {G : Type u_1} [inst : AddGroup G] {H : AddSubgroup G},
H.Characteristic ↔ ∀ (ϕ : G ≃+ G), H ≤ AddSubgroup.comap ϕ.toAddMonoidHom H- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
- Assumes
- AddGroup
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.
- DFunLike.coeproof · cited by 62,936
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- le_antisymmproof · cited by 2,068
- AddEquivstatement and proof · cited by 1,087
- AddEquiv.symmproof · cited by 530
- AddSubgroup.comapstatement and proof · cited by 123
- AddEquiv.toAddMonoidHomstatement and proof · cited by 101
- ge_of_eqproof · cited by 67
- AddEquiv.symm_apply_applyproof · cited by 19
- AddSubgroup.Characteristicstatement · cited by 17
- AddSubgroup.characteristic_iff_comap_eqproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.characteristic_iff_le_mapproof · cited by 0