Theorems · Theorem · group theory
IsCyclic.exponent_eq_card
∀ {α : Type u_1} [inst : Group α] [IsCyclic α], Monoid.exponent α = Nat.card α- Cited by
- 7 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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 and proof · cited by 844
- orderOfproof · cited by 324
- Monoid.exponentstatement and proof · cited by 128
- IsCyclicstatement and proof · cited by 122
- Monoid.order_dvd_exponentproof · cited by 14
- Group.exponent_dvd_nat_cardproof · cited by 4
- IsCyclic.exists_ofOrder_eq_natCardproof · cited by 3
Cited by7
Results whose statement or proof uses this declaration.
- IsCyclic.iff_exponent_eq_cardproof · cited by 6
- HasEnoughRootsOfUnity.natCard_rootsOfUnityproof · cited by 5
- Group.isCyclic_of_coprime_card_range_card_kerproof · cited by 1
- DihedralGroup.not_isCyclicproof · cited by 1
- IsZGroup.exponent_eq_cardproof · cited by 0
- not_isCyclic_iff_exponent_eq_primeproof · cited by 0
- IsKleinFour.not_isCyclicproof · cited by 0