Theorems · Definition · group theory
IsAddTorsion
(G : Type u_1) → [AddMonoid G] → Prop
A predicate on an additive monoid saying that all elements are of finite order.
- Defined in
- Mathlib.GroupTheory.Torsion
- Cited by
- 42 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- AddMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddMonoidstatement and proof · cited by 2,864
- IsOfFinAddOrderproof · cited by 105
Cited by47
Results whose statement or proof uses this declaration.
- IsAddTorsion.torsionAddEquivstatement and proof · cited by 4
- isAddTorsion_of_finitestatement · cited by 3
- IsAddTorsion.torsion_eq_topstatement and proof · cited by 3
- ExponentExists.isAddTorsionstatement · cited by 2
- AddCommGroup.finite_of_fg_isAddTorsionstatement and proof · cited by 2
- AddCommGroup.isAddTorsion_quotient_range_nsmulAddMonoidHomstatement · cited by 2
- isAddTorsion_iff_isTorsion_intstatement and proof · cited by 2
- IsAddTorsion.extension_closedstatement and proof · cited by 2
- IsAddTorsion.module_of_torsionstatement and proof · cited by 2
- IsAddTorsion.of_surjectivestatement and proof · cited by 2
- not_isAddTorsionFree_of_isAddTorsionstatement and proof · cited by 2
- AddCommGroup.freeRank_eq_zerostatement and proof · cited by 1