Theorems · Theorem · group theory
orderOf_eq_one_iff
∀ {G : Type u_1} [inst : Monoid G] {x : G}, orderOf x = 1 ↔ x = 1- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- mul_oneproof · cited by 3,885
- orderOfstatement · cited by 324
- Function.minimalPeriod_eq_one_iff_isFixedPtproof · cited by 5
Cited by12
Results whose statement or proof uses this declaration.
- exists_pow_eq_self_of_coprimeproof · cited by 3
- Monoid.exponent_eq_prime_iffproof · cited by 1
- NumberField.Units.torsion_eq_one_or_neg_one_of_odd_finrankproof · cited by 1
- IsPGroup.disjoint_of_coprimeproof · cited by 1
- IsPGroup.dvd_orderOfproof · cited by 1
- Equiv.Perm.cycleType_prime_orderproof · cited by 1
- ZMod.eq_one_or_isUnit_sub_oneproof · cited by 1
- NumberField.Units.rootsOfUnity_eq_oneproof · cited by 0
- Ideal.IsPrincipal.of_isPrincipal_pow_of_coprimeproof · cited by 0
- CommMonoid.primaryComponent.disjointproof · cited by 0
- not_isCyclic_iff_exponent_eq_primeproof · cited by 0
- FractionalIdeal.isPrincipal.of_isPrincipal_pow_of_coprimeproof · cited by 0