Theorems · Theorem · group theory
IsCyclic.iff_exponent_eq_card
∀ {α : Type u_1} [inst : CommGroup α] [Finite α], IsCyclic α ↔ Monoid.exponent α = Nat.card α- Cited by
- 6 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finitestatement and proof · cited by 3,029
- CommGroupstatement and proof · cited by 990
- Nat.cardstatement · cited by 844
- Monoid.exponentstatement · cited by 128
- IsCyclicstatement and proof · cited by 122
- IsCyclic.exponent_eq_cardproof · cited by 7
- IsCyclic.of_exponent_eq_cardproof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- ZMod.not_isCyclic_units_eightproof · cited by 2
- Group.isCyclic_of_coprime_card_range_card_kerproof · cited by 1
- coprime_card_of_isCyclic_prodproof · cited by 1
- ArithmeticFunction.carmichael_two_pow_of_le_two_eq_totientproof · cited by 1
- ArithmeticFunction.carmichael_two_pow_of_ne_twoproof · cited by 1
- ArithmeticFunction.carmichael_pow_of_prime_ne_twoproof · cited by 0