Theorems · Theorem · group theory
IsAddCyclic.exponent_eq_card
∀ {α : Type u_1} [inst : AddGroup α] [IsAddCyclic α], AddMonoid.exponent α = Nat.card α- Cited by
- 5 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroupIsAddCyclic
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.
- AddGroupstatement and proof · cited by 4,410
- Nat.cardstatement and proof · cited by 844
- addOrderOfproof · cited by 208
- AddMonoid.exponentstatement and proof · cited by 70
- IsAddCyclicstatement and proof · cited by 55
- AddMonoid.addOrder_dvd_exponentproof · cited by 10
- AddGroup.exponent_dvd_nat_cardproof · cited by 2
- IsAddCyclic.exists_ofOrder_eq_natCardproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- IsAddCyclic.iff_exponent_eq_cardproof · cited by 2
- AddGroup.isAddCyclic_of_coprime_card_range_card_kerproof · cited by 1
- ZMod.exponentproof · cited by 0
- not_isAddCyclic_iff_exponent_eq_primeproof · cited by 0
- IsAddKleinFour.not_isAddCyclicproof · cited by 0