Theorems · Theorem · group theory
isSimpleGroup_of_prime_card
∀ {α : Type u_1} [inst : Group α] {p : ℕ} [hp : Fact (Nat.Prime p)], Nat.card α = p → IsSimpleGroup αA finite group of prime order is simple.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Subgroupproof · cited by 3,593
- 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
- Subgroup.Normalproof · cited by 334
- Fact.outproof · cited by 328
- Nat.Prime.one_ltproof · cited by 118
- Nat.Prime.ne_zeroproof · cited by 109
- Nat.finite_of_card_ne_zeroproof · cited by 33
Cited by1
Results whose statement or proof uses this declaration.
- Group.is_simple_iff_prime_cardproof · cited by 1