Theorems · Theorem · group theory
alternatingGroup.isPretransitive_of_three_le_card
∀ (α : Type u_1) [inst : Fintype α] [inst_1 : DecidableEq α], 3 ≤ Nat.card α → MulAction.IsPretransitive (↥(alternatingGroup α)) α
The alternating group on 3 letters or more acts transitively.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Subgroupstatement · cited by 3,593
- Equiv.Permstatement and proof · cited by 1,375
- le_transproof · cited by 985
- Nat.cardstatement and proof · cited by 844
- alternatingGroupstatement and proof · cited by 96
- MulAction.IsPretransitivestatement · cited by 94
- add_le_add_iff_rightproof · cited by 47
- MulAction.IsMultiplyPretransitiveproof · cited by 33
- MulAction.is_one_pretransitive_iffproof · cited by 7
- MulAction.isMultiplyPretransitive_of_leproof · cited by 6
- alternatingGroup.isMultiplyPretransitiveproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- alternatingGroup.isTrivialBlock_of_isBlockproof · cited by 1
- Set.powersetCard.isPretransitive_alternatingGroupproof · cited by 1