Theorems · Theorem · group theory
isCyclic_of_card_dvd_prime
∀ {α : Type u_1} [inst : Group α] {p : ℕ} [hp : Fact (Nat.Prime p)], Nat.card α ∣ p → IsCyclic αA finite group of order dividing a prime is cyclic.
- Cited by
- 4 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.
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
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- Nat.cardstatement and proof · cited by 844
- Fact.outproof · cited by 328
- IsCyclicstatement · cited by 122
- Nat.dvd_primeproof · cited by 18
- isCyclic_of_prime_cardproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- Equiv.Perm.isCyclic_of_card_le_twoproof · cited by 1
- IsPGroup.cyclic_center_quotient_of_card_eq_prime_sqproof · cited by 1
- alternatingGroup.isCyclic_of_card_le_threeproof · cited by 1
- IsZGroup.of_squarefreeproof · cited by 0