Theorems · Theorem · group theory
addOrderOf_injective
∀ {G : Type u_1} [inst : AddMonoid G] {H : Type u_6} [inst_1 : AddMonoid H] (f : G →+ H),
Function.Injective ⇑f → ∀ (x : G), addOrderOf (f x) = addOrderOf xAn injective homomorphism of additive monoids preserves orders of elements.
- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- DFunLike.coestatement and proof · cited by 62,936
- AddMonoidHomstatement and proof · cited by 3,230
- AddMonoidstatement and proof · cited by 2,864
- addOrderOfstatement · cited by 208
- AddMonoidHom.map_zeroproof · cited by 47
- AddMonoidHom.map_nsmulproof · cited by 18
- addOrderOf_eq_addOrderOf_iffproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- Function.Injective.isOfFinAddOrder_iffproof · cited by 2
- AddSubgroup.addOrderOf_coeproof · cited by 1
- addOrderOf_addSubmonoidproof · cited by 1
- AddEquiv.addOrderOf_eqproof · cited by 0
- addOrderOf_addUnitsproof · cited by 0