Theorems · Theorem · group theory
AddSubgroup.nsmulAddMonoidHom_injective_of_isTorsionFree
∀ {M : Type u_1} [inst : AddCommGroup M] [Module.IsTorsionFree ℤ M] {n : ℕ},
n ≠ 0 → Function.Injective ⇑(nsmulAddMonoidHom n)On an additive group that is torsion-free as a ℤ-module, the multiplication-by-n map
is injective (when n ≠ 0).
- Defined in
- Mathlib.GroupTheory.IndexNSmul
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- AddCommGroupstatement and proof · cited by 12,871
- AddMonoidHomstatement · cited by 3,230
- Module.IsTorsionFreestatement and proof · cited by 600
- AddMonoidHom.kerproof · cited by 158
- nsmulAddMonoidHomstatement and proof · cited by 24
- AddMonoidHom.ker_eq_bot_iffproof · cited by 14
- AddSubgroup.eq_bot_iff_forallproof · cited by 11
- nsmulAddMonoidHom_applyproof · cited by 9
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