Theorems · Theorem · group theory
AddMonoid.exponent_dvd_of_addMonoidHom
∀ {G : Type u} [inst : AddMonoid G] {H : Type u_1} [inst_1 : AddMonoid H] (e : G →+ H),
Function.Injective ⇑e → AddMonoid.exponent G ∣ AddMonoid.exponent HIf there exists an injective, addition-preserving map from G to H,
then the exponent of G divides the exponent of H.
- Defined in
- Mathlib.GroupTheory.Exponent
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- AddMonoidHomstatement and proof · cited by 3,230
- AddMonoidstatement and proof · cited by 2,864
- map_zeroproof · cited by 1,614
- AddMonoid.exponentstatement and proof · cited by 70
- map_nsmulproof · cited by 41
- AddMonoid.exponent_nsmul_eq_zeroproof · cited by 12
- AddMonoid.exponent_dvd_of_forall_nsmul_eq_zeroproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- AddMonoid.exponent_eq_of_addEquivproof · cited by 3
- AddGroup.isAddCyclic_of_coprime_card_range_card_kerproof · cited by 1
- AddMonoid.exponent_addSubmonoid_dvdproof · cited by 0