Theorems · Theorem · group theory
MulAction.IsPreprimitive.is_two_pretransitive
∀ {G : Type u_1} {α : Type u_2} [inst : Group G] [inst_1 : MulAction G α],
MulAction.IsPreprimitive G α →
∀ {s : Set α} {n : ℕ},
s.ncard = n + 1 →
n + 2 < Nat.card α →
MulAction.IsPretransitive ↥(fixingSubgroup G s) ↥(SubMulAction.ofFixingSubgroup G s) →
MulAction.IsMultiplyPretransitive G α 2A criterion due to Jordan for being 2-pretransitive (Wielandt, 13.1)
- Defined in
- Mathlib.GroupTheory.GroupAction.Jordan
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites13
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
- Groupstatement and proof · cited by 6,238
- Subgroupstatement · cited by 3,593
- MulActionstatement and proof · cited by 1,294
- Nat.cardstatement and proof · cited by 844
- Set.ncardstatement and proof · cited by 344
- SubMulActionstatement · cited by 120
- MulAction.IsPretransitivestatement and proof · cited by 94
- fixingSubgroupstatement and proof · cited by 83
- MulAction.IsPreprimitivestatement and proof · cited by 50
- SubMulAction.ofFixingSubgroupstatement and proof · cited by 43
- MulAction.IsMultiplyPretransitivestatement · cited by 33
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