Theorems · Theorem · group theory
Group.exponent_dvd_nat_card
∀ {G : Type u} [inst : Group G], Monoid.exponent G ∣ Nat.card G- Defined in
- Mathlib.GroupTheory.Exponent
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
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.
- Groupstatement and proof · cited by 6,238
- Nat.cardstatement · cited by 844
- Monoid.exponentstatement · cited by 128
- orderOf_dvd_natCardproof · cited by 14
- Monoid.exponent_dvdproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- IsCyclic.exponent_eq_cardproof · cited by 7
- Group.isCyclic_of_coprime_card_range_card_kerproof · cited by 1
- ArithmeticFunction.carmichael_two_pow_of_ne_twoproof · cited by 1
- IsZGroup.exponent_eq_cardproof · cited by 0