Theorems · Theorem · group theory
AddSubgroup.characteristic_iff_map_le
∀ {G : Type u_1} [inst : AddGroup G] {H : AddSubgroup G},
H.Characteristic ↔ ∀ (ϕ : G ≃+ G), AddSubgroup.map ϕ.toAddMonoidHom H ≤ H- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
- Assumes
- AddGroup
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Cites10
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 and proof · cited by 1,087
- AddEquiv.symmproof · cited by 530
- AddSubgroup.mapstatement · cited by 189
- AddSubgroup.comapproof · cited by 123
- AddEquiv.toAddMonoidHomstatement and proof · cited by 101
- AddSubgroup.Characteristicstatement and proof · cited by 17
- AddSubgroup.map_equiv_eq_comap_symm'proof · cited by 4
- AddSubgroup.characteristic_iff_comap_leproof · cited by 1
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