Theorems · Definition · group theory
IsOfFinOrder
{G : Type u_1} → [Monoid G] → G → PropIsOfFinOrder is a predicate on an element x of a monoid to be of finite order, i.e. there
exists n ≥ 1 such that x ^ n = 1.
- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 113 results in Mathlib
- Foundations
- Depth 9 from the axioms, rests on 52 definitions · uses no axioms
- Assumes
- Monoid
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.
- Monoidstatement and proof · cited by 3,887
- Function.periodicPtsproof · cited by 33
Cited by120
Results whose statement or proof uses this declaration.
- IsMulTorsionproof · cited by 35
- isOfFinOrder_iff_pow_eq_onestatement · cited by 27
- IsOfFinOrder.orderOf_posstatement and proof · cited by 17
- isOfFinOrder_of_finitestatement and proof · cited by 14
- CommMonoid.torsionproof · cited by 12
- finEquivPowersstatement and proof · cited by 9
- orderOf_eq_zero_iffstatement and proof · cited by 8
- orderOf_pos_iffstatement · cited by 8
- Monoid.minOrderproof · cited by 7
- CommGroup.mem_torsionstatement · cited by 6
- finEquivZPowersstatement and proof · cited by 6
- MonoidHom.isOfFinOrderstatement and proof · cited by 6