Theorems · Theorem · group theory
Monoid.exponent_dvd
∀ {G : Type u} [inst : Monoid G] {n : ℕ}, Monoid.exponent G ∣ n ↔ ∀ (g : G), orderOf g ∣ n- Defined in
- Mathlib.GroupTheory.Exponent
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 76 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.
Cites3
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 and proof · cited by 324
- Monoid.exponentstatement · cited by 128
Cited by6
Results whose statement or proof uses this declaration.
- Group.exponent_dvd_nat_cardproof · cited by 4
- Monoid.exponent_ne_zero_iff_range_orderOf_finiteproof · cited by 3
- Monoid.lcm_orderOf_eq_exponentproof · cited by 1
- Monoid.exponent_eq_prime_iffproof · cited by 1
- alternatingGroup.exponent_kleinFour_of_card_eq_fourproof · cited by 1
- Group.exponent_dvd_cardproof · cited by 1