Theorems · Theorem · group theory
isCyclic_of_prime_card
∀ {α : Type u_1} [inst : Group α] {p : ℕ} [hp : Fact (Nat.Prime p)], Nat.card α = p → IsCyclic αA finite group of prime order is cyclic.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Finiteproof · cited by 3,029
- Factstatement and proof · cited by 2,726
- Nontrivialproof · cited by 2,416
- 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.Prime.one_ltproof · cited by 118
- Nat.Prime.ne_zeroproof · cited by 109
- exists_neproof · cited by 101
- Nat.finite_of_card_ne_zeroproof · cited by 33
Cited by4
Results whose statement or proof uses this declaration.
- isCyclic_of_card_dvd_primeproof · cited by 4
- DihedralGroup.isCyclic_iffproof · cited by 0
- mulEquivOfPrimeCardEqproof · cited by 0
- ZMod.isCyclic_units_fourproof · cited by 0