Theorems · Theorem · group theory
pow_eq_one_iff_modEq
∀ {G : Type u_1} [inst : Monoid G] {x : G} {n : ℕ}, x ^ n = 1 ↔ n ≡ 0 [MOD orderOf x]- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 33 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.
Cites5
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
- Nat.ModEqstatement · cited by 225
- orderOf_dvd_iff_pow_eq_oneproof · cited by 22
- Nat.modEq_zero_iff_dvdproof · cited by 17
Cited by3
Results whose statement or proof uses this declaration.
- pow_eq_pow_iff_modEqproof · cited by 5
- RightCancelMonoid.pow_eq_pow_iff_modEqproof · cited by 3
- IsOfFinOrder.pow_eq_pow_iff_modEqproof · cited by 1