Theorems · Theorem · group theory
Monoid.order_dvd_exponent
∀ {G : Type u} [inst : Monoid G] (g : G), orderOf g ∣ Monoid.exponent G- Defined in
- Mathlib.GroupTheory.Exponent
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 32 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.
Cites5
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 · cited by 324
- Monoid.exponentstatement · cited by 128
- orderOf_dvd_of_pow_eq_oneproof · cited by 24
- Monoid.pow_exponent_eq_oneproof · cited by 13
Cited by14
Results whose statement or proof uses this declaration.
- IsCyclic.exponent_eq_cardproof · cited by 7
- HasEnoughRootsOfUnity.natCard_rootsOfUnityproof · cited by 5
- Monoid.exponent_prodproof · cited by 2
- Monoid.ExponentExists.of_finiteproof · cited by 2
- Monoid.orderOf_le_exponentproof · cited by 1
- Monoid.exponent_eq_prime_iffproof · cited by 1
- Monoid.lcm_orderOf_dvd_exponentproof · cited by 1
- ArithmeticFunction.carmichael_two_pow_of_ne_twoproof · cited by 1
- mul_comm_of_exponent_twoproof · cited by 1
- DihedralGroup.exponentproof · cited by 1
- card_dvd_exponent_pow_rankproof · cited by 1
- Monoid.exists_orderOf_eq_exponentproof · cited by 1