Theorems · Theorem · group theory
IsOfFinOrder.orderOf_pow
∀ {G : Type u_1} [inst : Monoid G] (x : G) (n : ℕ), IsOfFinOrder x → orderOf (x ^ n) = orderOf x / (orderOf x).gcd n- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 36 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.
Cites6
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
- IsOfFinOrderstatement and proof · cited by 113
- Function.minimalPeriodproof · cited by 100
- mul_left_iterateproof · cited by 11
- Function.minimalPeriod_iterate_eq_div_gcd'proof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- orderOf_powproof · cited by 5
- Nat.Coprime.orderOf_powproof · cited by 1