Theorems · Theorem · group theory
SubAddAction.ofFixingAddSubgroup.isMultiplyPretransitive
∀ (G : Type u_1) {α : Type u_2} [inst : AddGroup G] [inst_1 : AddAction G α] {m n : ℕ}
[Hn : AddAction.IsMultiplyPretransitive G α n] (s : Set α) [Finite ↑s],
s.ncard + m = n →
AddAction.IsMultiplyPretransitive (↥(fixingAddSubgroup G s)) (↥(SubAddAction.ofFixingAddSubgroup G s)) mThe fixingSubgroup of a finite subset of cardinal d
in an n-transitive additive action acts n-d-transitively on the complement.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites28
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Equiv.apply_symm_applyproof · cited by 346
Cited by3
Results whose statement or proof uses this declaration.
- AddAction.isMultiplyPreprimitive_of_isMultiplyPretransitive_succproof · cited by 1
- AddAction.ofFixingSubgroup.isMultiplyPreprimitiveproof · cited by 0
- SubAddAction.ofFixingAddSubgroup.isMultiplyPretransitive'proof · cited by 0