Theorems · Theorem · group theory
MulAction.IsPreprimitive.of_prime_card
∀ {G : Type u_1} {X : Type u_2} [inst : Group G] [inst_1 : MulAction G X] [hGX : MulAction.IsPretransitive G X],
Nat.Prime (Nat.card X) → MulAction.IsPreprimitive G XA pretransitive action on a set of prime order is preprimitive
- 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.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Groupstatement and proof · cited by 6,238
- Finiteproof · cited by 3,029
- Nat.Primestatement and proof · cited by 2,059
- LT.lt.ne'proof · cited by 1,417
- MulActionstatement and proof · cited by 1,294
- Nat.cardstatement and proof · cited by 844
- Set.toFiniteproof · cited by 174
- Set.Nontrivialproof · cited by 145
- Nat.Prime.ne_zeroproof · cited by 109
- MulAction.IsPretransitivestatement and proof · cited by 94
- MulAction.IsBlockproof · cited by 73
Cited by3
Results whose statement or proof uses this declaration.
- Equiv.Perm.alternatingGroup_le_of_isPreprimitive_of_isThreeCycle_memproof · cited by 2
- alternatingGroup.isTrivialBlock_of_isBlockproof · cited by 1
- Equiv.Perm.subgroup_eq_top_of_isPreprimitive_of_isSwap_memproof · cited by 1