Theorems · Theorem · group theory
isPeriodicPt_mul_iff_pow_eq_one
∀ {G : Type u_1} [inst : Monoid G] {n : ℕ} (x : G), Function.IsPeriodicPt (fun x_1 => x * x_1) n 1 ↔ x ^ n = 1- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, 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
- Nat.iterateproof · cited by 740
- Function.IsPeriodicPtstatement · cited by 68
- mul_left_iterate_apply_oneproof · cited by 3
Cited by11
Results whose statement or proof uses this declaration.
- orderOf_dvd_of_pow_eq_oneproof · cited by 24
- pow_ne_one_of_lt_orderOfproof · cited by 4
- orderOf_eq_prime_powproof · cited by 4
- orderOf_le_of_pow_eq_oneproof · cited by 3
- orderOf_eq_prime_iffproof · cited by 3
- neg_one_mem_torsionproof · cited by 2
- IsPrimitiveRoot.isOfFinOrderproof · cited by 2
- NumberField.Units.dvd_torsionOrder_of_isPrimitiveRootproof · cited by 1
- isPrimitiveRoot_of_mem_rootsOfUnityproof · cited by 1
- CommMonoid.torsion.isMulTorsionproof · cited by 1
- exists_zpow_eq_oneproof · cited by 0