Theorems · Theorem · group theory
orderOf_pow_of_dvd
∀ {G : Type u_1} [inst : Monoid G] {x : G} {n : ℕ}, n ≠ 0 → n ∣ orderOf x → orderOf (x ^ n) = orderOf x / n- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 37 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.
Cites3
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 and proof · cited by 324
- orderOf_pow'proof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- IsPrimitiveRoot.pow_of_dvdproof · cited by 4
- orderOf_pow_orderOf_divproof · cited by 2