Theorems · Theorem · group theory
IsUnit.of_pow_eq_one
∀ {M : Type u_1} [inst : Monoid M] {n : ℕ} {a : M}, a ^ n = 1 → n ≠ 0 → IsUnit a- Defined in
- Mathlib.Algebra.Group.Commute.Units
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- IsUnitstatement · cited by 1,602
- Units.isUnitproof · cited by 116
- Units.ofPowEqOneproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- IsPrimitiveRoot.eq_pow_of_pow_eq_oneproof · cited by 17
- Polynomial.isUnitTrinomial_iff'proof · cited by 1
- orderOf_lt_cardproof · cited by 1
- pow_gcd_eq_oneproof · cited by 0