Theorems · Definition · group theory
IsOfFinAddOrder
{G : Type u_1} → [AddMonoid G] → G → PropIsOfFinAddOrder is a predicate on an element a of an
additive monoid to be of finite order, i.e. there exists n ≥ 1 such that n • a = 0.
- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 105 results in Mathlib
- Foundations
- Depth 9 from the axioms, rests on 52 definitions · 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
- Function.periodicPtsproof · cited by 33
Cited by112
Results whose statement or proof uses this declaration.
- IsAddTorsionproof · cited by 42
- isOfFinAddOrder_iff_nsmul_eq_zerostatement · cited by 27
- IsOfFinAddOrder.addOrderOf_posstatement and proof · cited by 16
- AddCommMonoid.addTorsionproof · cited by 12
- isOfFinAddOrder_of_finitestatement and proof · cited by 10
- addOrderOf_pos_iffstatement · cited by 10
- addOrderOf_eq_zero_iffstatement and proof · cited by 9
- AddMonoid.minOrderproof · cited by 9
- finEquivMultiplesstatement and proof · cited by 7
- not_isOfFinAddOrder_of_isAddTorsionFreestatement · cited by 7
- IsOfFinAddOrder.exists_nsmul_eq_zerostatement · cited by 6
- finEquivZMultiplesstatement and proof · cited by 5