Theorems · Theorem · group theory
Set.powersetCard.isPreprimitive_perm
∀ {α : Type u_2} [inst : DecidableEq α] {n : ℕ},
1 ≤ n → n < Nat.card α → Nat.card α ≠ 2 * n → MulAction.IsPreprimitive (Equiv.Perm α) ↑(Set.powersetCard α n)The action of Equiv.Perm α on Set.powersetCard α n is preprimitive
provided 1 ≤ n < Nat.card α and Nat.card α ≠ 2 * n.
This is a consequence that the stabilizer of such a combination
is a maximal subgroup.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- SetLike.coeproof · cited by 8,199
- Fintypeproof · cited by 7,736
- Set.Elemstatement and proof · cited by 7,166
- Set.univproof · cited by 3,945
- Subgroupproof · cited by 3,593
- Finiteproof · cited by 3,029
- Nontrivialproof · cited by 2,416
- Equiv.Permstatement and proof · cited by 1,375
- LT.lt.neproof · cited by 872
- Nat.cardstatement and proof · cited by 844
- Fintype.ofFiniteproof · cited by 255
Cited by1
Results whose statement or proof uses this declaration.
- Equiv.Perm.alternatingGroup_le_of_normalproof · cited by 0