Theorems · Theorem · group theory
isUnit_pow_iff
∀ {M : Type u_1} [inst : Monoid M] {n : ℕ} {a : M}, n ≠ 0 → (IsUnit (a ^ n) ↔ IsUnit a)- Defined in
- Mathlib.Algebra.Group.Commute.Units
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Unitsproof · cited by 2,804
- Units.valproof · cited by 1,966
- IsUnitstatement and proof · cited by 1,602
- Units.isUnitproof · cited by 116
- IsUnit.powproof · cited by 48
- Units.ofPowproof · cited by 1
Cited by7
Results whose statement or proof uses this declaration.
- not_irreducible_powproof · cited by 6
- IsPrimePow.not_isUnitproof · cited by 2
- RingOfIntegers.isUnit_normproof · cited by 1
- isUnit_pow_succ_iffproof · cited by 1
- IsPrimitiveRoot.prime_dvd_of_dvd_norm_sub_oneproof · cited by 1
- Matrix.inv_kroneckerproof · cited by 0
- fermatLastTheoremWith'_nat_int_tfaeproof · cited by 0