Theorems · Theorem · group theory
alternatingGroup.isTrivialBlock_of_isBlock
∀ (α : Type u_1) [inst : Fintype α] [inst_1 : DecidableEq α] {B : Set α},
MulAction.IsBlock (↥(alternatingGroup α)) B → MulAction.IsTrivialBlock BThe action of the alternating group has trivial blocks.
This holds for any α, even when Nat.card α ≤ 2 and the action
is not preprimitive, because it is not pretransitive.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 107 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.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Fintypestatement and proof · cited by 7,736
- Subgroupstatement · cited by 3,593
- le_antisymmproof · cited by 2,068
- Equiv.Permstatement and proof · cited by 1,375
- le_of_ltproof · cited by 1,175
- Nat.cardproof · cited by 844
- Eq.geproof · cited by 375
- le_or_gtproof · cited by 269
- alternatingGroupstatement and proof · cited by 96
- MulAction.IsPretransitiveproof · cited by 94
- MulAction.IsBlockstatement and proof · cited by 73
Cited by1
Results whose statement or proof uses this declaration.
- alternatingGroup.isPreprimitive_of_three_le_cardproof · cited by 1