Theorems · Theorem · group theory
isOfFinOrder_iff_pow_eq_one
∀ {G : Type u_1} [inst : Monoid G] {x : G}, IsOfFinOrder x ↔ ∃ n, 0 < n ∧ x ^ n = 1- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Quot.sound
- 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
- IsOfFinOrderstatement · cited by 113
Cited by27
Results whose statement or proof uses this declaration.
- MonoidHom.isOfFinOrderproof · cited by 6
- not_isOfFinOrder_of_isMulTorsionFreeproof · cited by 4
- IsOfFinOrder.exists_pow_eq_oneproof · cited by 4
- MulChar.orderOf_posproof · cited by 3
- ExponentExists.isMulTorsionproof · cited by 2
- NumberField.Units.mem_torsionproof · cited by 2
- IsMulTorsion.extension_closedproof · cited by 2
- Module.Dual.eq_of_preReflection_mapsToproof · cited by 2
- orderOf_eq_of_pow_and_pow_div_primeproof · cited by 2
- NumberField.Units.rootsOfUnity_eq_torsionproof · cited by 2
- IsPrimitiveRoot.exists_posproof · cited by 2
- IsOfFinOrder.zpowproof · cited by 1