Theorems · Theorem · group theory
alternatingGroup.isMultiplyPretransitive
∀ (α : Type u_1) [inst : Fintype α] [inst_1 : DecidableEq α], MulAction.IsMultiplyPretransitive (↥(alternatingGroup α)) α (Nat.card α - 2)
The alternatingGroup on α is (Nat.card α - 2)-pretransitive.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 105 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.
Cites44
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Finsetproof · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- mul_oneproof · cited by 3,885
- Subgroupstatement · cited by 3,593
- Finset.univproof · cited by 3,473
- Compl.complproof · cited by 2,925
- Finset.cardproof · cited by 2,327
- le_rflproof · cited by 1,558
- Fintype.cardproof · cited by 1,386
- Equiv.Permstatement and proof · cited by 1,375
- le_of_ltproof · cited by 1,175
Cited by4
Results whose statement or proof uses this declaration.
- alternatingGroup.isPretransitive_of_three_le_cardproof · cited by 2
- alternatingGroup.isTrivialBlock_of_isBlockproof · cited by 1
- alternatingGroup.isCoatom_stabilizer_of_ncard_lt_ncard_complproof · cited by 1
- Set.powersetCard.isPretransitive_alternatingGroupproof · cited by 1