Theorems · Theorem · group theory
Nat.Coprime.orderOf_pow
∀ {G : Type u_1} [inst : Monoid G] {y : G} {m : ℕ}, (orderOf y).Coprime m → orderOf (y ^ m) = orderOf y- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 1 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.
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
- pow_oneproof · cited by 894
- orderOfstatement and proof · cited by 324
- IsOfFinOrderproof · cited by 113
- orderOf_eq_zeroproof · cited by 5
- IsOfFinOrder.orderOf_powproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- approxOrderOf.image_pow_subset_of_coprimeproof · cited by 0