Theorems · Theorem · group theory
CommGroup.isMulTorsion_quotient_range_powMonoidHom
∀ (G : Type u_1) [inst : CommGroup G] {n : ℕ}, n ≠ 0 → IsMulTorsion (G ⧸ (powMonoidHom 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
- CommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Subgroupstatement · cited by 3,593
- HasQuotient.Quotientstatement and proof · cited by 2,301
- CommGroupstatement and proof · cited by 990
- MonoidHom.rangestatement and proof · cited by 314
- powMonoidHomstatement and proof · cited by 35
- IsMulTorsionstatement · cited by 35
- QuotientGroup.eq_one_iffproof · cited by 18
- QuotientGroup.induction_onproof · cited by 17
- Ne.posproof · cited by 17
- powMonoidHom_applyproof · cited by 11
- QuotientGroup.mk_powproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Subgroup.finiteIndex_range_powMonoidHom_of_fgproof · cited by 1
- CommGroup.isTorsion_quotient_range_powMonoidHomproof · cited by 0