Theorems · Theorem · group theory
AddMonoid.exponent_dvd
∀ {G : Type u} [inst : AddMonoid G] {n : ℕ}, AddMonoid.exponent G ∣ n ↔ ∀ (g : G), addOrderOf g ∣ n- Defined in
- Mathlib.GroupTheory.Exponent
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddMonoid
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.
- AddMonoidstatement and proof · cited by 2,864
- addOrderOfstatement and proof · cited by 208
- AddMonoid.exponentstatement · cited by 70
- addOrderOf_dvd_iff_nsmul_eq_zeroproof · cited by 17
- AddMonoid.exponent_dvd_iff_forall_nsmul_eq_zeroproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- AddMonoid.exponent_ne_zero_iff_range_addOrderOf_finiteproof · cited by 3
- AddGroup.exponent_dvd_nat_cardproof · cited by 2
- AddMonoid.lcm_addOrderOf_eq_exponentproof · cited by 1
- AddMonoid.exponent_eq_prime_iffproof · cited by 1
- AddGroup.exponent_dvd_cardproof · cited by 1