Theorems · Theorem · group theory
IsSimpleGroup.prime_card
∀ {α : Type u_1} [inst : CommGroup α] [IsSimpleGroup α], Nat.Prime (Nat.card α)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommGroupIsSimpleGroup
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.
- Top.topproof · cited by 9,680
- Nontrivialproof · cited by 2,416
- Nat.Primestatement and proof · cited by 2,059
- CommGroupstatement and proof · cited by 990
- Nat.cardstatement and proof · cited by 844
- orderOfproof · cited by 324
- Subgroup.zpowersproof · cited by 204
- IsSimpleOrder.eq_bot_or_eq_topproof · cited by 32
- IsSimpleGroupstatement and proof · cited by 26
- Nat.card_eq_one_iff_uniqueproof · cited by 15
- IsCyclic.exists_generatorproof · cited by 14
- orderOf_eq_card_of_forall_mem_zpowersproof · cited by 13
Cited by3
Results whose statement or proof uses this declaration.
- Group.is_simple_iff_prime_cardproof · cited by 1
- IsSimpleGroup.finiteproof · cited by 0
- exists_prime_addEquiv_ZModproof · cited by 0