Theorems · Theorem · group theory
AddSubgroup.characteristic_iff_comap_eq
∀ {G : Type u_1} [inst : AddGroup G] {H : AddSubgroup G},
H.Characteristic ↔ ∀ (ϕ : G ≃+ G), AddSubgroup.comap ϕ.toAddMonoidHom H = H- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddEquivstatement · cited by 1,087
- AddSubgroup.comapstatement · cited by 123
- AddEquiv.toAddMonoidHomstatement · cited by 101
- AddSubgroup.Characteristicstatement · cited by 17
- AddSubgroup.Characteristic.fixedproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- AddSubgroup.characteristic_iff_map_eqproof · cited by 1
- AddSubgroup.characteristic_iff_comap_leproof · cited by 1
- AddSubgroup.characteristic_iff_le_comapproof · cited by 1
- AddSubgroup.Characteristic.comap_quotient_mkproof · cited by 0