Theorems · Theorem · group theory
pow_eq_one_iff_right
∀ {M : Type u_1} [inst : Monoid M] [IsMulTorsionFree M] {n : ℕ} {a : M}, a ≠ 1 → (a ^ n = 1 ↔ n = 0)- Defined in
- Mathlib.Algebra.Group.Torsion
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MonoidIsMulTorsionFree
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
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
- IsMulTorsionFreestatement and proof · cited by 44
Cited by1
Results whose statement or proof uses this declaration.
- IsLeftRegular.pow_injectiveproof · cited by 4