Theorems · Theorem · group theory
AddCommGroup.isAddTorsion_quotient_range_nsmulAddMonoidHom
∀ (G : Type u_1) [inst : AddCommGroup G] {n : ℕ}, n ≠ 0 → IsAddTorsion (G ⧸ (nsmulAddMonoidHom n).range)- Defined in
- Mathlib.GroupTheory.Torsion
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommGroupstatement and proof · cited by 12,871
- AddSubgroupstatement · cited by 3,232
- HasQuotient.Quotientstatement and proof · cited by 2,301
- AddMonoidHom.rangestatement and proof · cited by 142
- IsAddTorsionstatement · cited by 42
- QuotientAddGroup.induction_onproof · cited by 33
- isOfFinAddOrder_iff_nsmul_eq_zeroproof · cited by 27
- nsmulAddMonoidHomstatement and proof · cited by 24
- QuotientAddGroup.eq_zero_iffproof · cited by 19
- Ne.posproof · cited by 17
- AddMonoidHom.mem_rangeproof · cited by 16
- nsmulAddMonoidHom_applyproof · cited by 9
Cited by2
Results whose statement or proof uses this declaration.
- AddSubgroup.finiteIndex_range_nsmulAddMonoidHom_of_fgproof · cited by 1
- AddCommGroup.isTorsion_quotient_range_nsmulAddMonoidHomproof · cited by 0