Theorems · Theorem · group theory
Group.is_simple_iff_prime_card
∀ {α : Type u_1} [inst : Group α] [IsMulCommutative α], IsSimpleGroup α ↔ Nat.Prime (Nat.card α)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupIsMulCommutative
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.
- Groupstatement and proof · cited by 6,238
- Nat.Primestatement and proof · cited by 2,059
- Nat.cardstatement and proof · cited by 844
- IsMulCommutativestatement and proof · cited by 95
- IsSimpleGroupstatement and proof · cited by 26
- IsSimpleGroup.prime_cardproof · cited by 3
- isSimpleGroup_of_prime_cardproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- CommGroup.is_simple_iff_prime_cardproof · cited by 0