Theorems · Theorem · group theory
orderOf_dvd_of_pow_eq_one
∀ {G : Type u_1} [inst : Monoid G] {x : G} {n : ℕ}, x ^ n = 1 → orderOf x ∣ n- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 31 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
- orderOfstatement · cited by 324
- isPeriodicPt_mul_iff_pow_eq_oneproof · cited by 11
- Function.IsPeriodicPt.minimalPeriod_dvdproof · cited by 4
Cited by24
Results whose statement or proof uses this declaration.
- orderOf_dvd_iff_pow_eq_oneproof · cited by 22
- IsPrimitiveRoot.map_of_injectiveproof · cited by 19
- Monoid.order_dvd_exponentproof · cited by 14
- IsPrimitiveRoot.orderOfproof · cited by 10
- orderOf_map_dvdproof · cited by 3
- Equiv.Perm.card_compl_support_modEqproof · cited by 3
- QuaternionGroup.orderOf_a_oneproof · cited by 2
- ZMod.orderOf_dvd_card_sub_oneproof · cited by 2
- FiniteField.unit_isSquare_iffproof · cited by 2
- orderOf_eq_of_pow_and_pow_div_primeproof · cited by 2
- IsPrimitiveRoot.of_map_of_injectiveproof · cited by 2
- IsCyclic.card_pow_eq_one_leproof · cited by 2