Theorems · Theorem · group theory
IsSimpleAddGroup.prime_card
∀ {α : Type u_1} [inst : AddCommGroup α] [IsSimpleAddGroup α], Nat.Prime (Nat.card α)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommGroupIsSimpleAddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommGroupstatement and proof · cited by 12,871
- Top.topproof · cited by 9,680
- Nontrivialproof · cited by 2,416
- Nat.Primestatement and proof · cited by 2,059
- Nat.cardstatement and proof · cited by 844
- AddSubgroup.zmultiplesproof · cited by 493
- addOrderOfproof · cited by 208
- zero_dvd_iffproof · cited by 37
- IsSimpleOrder.eq_bot_or_eq_topproof · cited by 32
- AddSubgroup.mem_topproof · cited by 29
- not_nontrivial_iff_subsingletonproof · cited by 23
- OfNat.ofNat_ne_zeroproof · cited by 20
Cited by2
Results whose statement or proof uses this declaration.
- AddGroup.is_simple_iff_prime_cardproof · cited by 1
- IsSimpleAddGroup.finiteproof · cited by 0