Theorems · Theorem · group theory

SubMulAction.ofStabilizer.isMultiplyPretransitive_iff

∀ {G : Type u_1} {α : Type u_2} [inst : Group G] [inst_1 : MulAction G α] [MulAction.IsPretransitive G α] {n : ℕ}
  {a b : α},
  MulAction.IsMultiplyPretransitive (↥(MulAction.stabilizer G a)) (↥(SubMulAction.ofStabilizer G a)) n ↔
    MulAction.IsMultiplyPretransitive (↥(MulAction.stabilizer G b)) (↥(SubMulAction.ofStabilizer G b)) n

Defined in: Mathlib.GroupTheory.GroupAction.MultipleTransitivity
Cited by: 0 results in Mathlib
Foundations: Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Group MulAction MulAction.IsPretransitive

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Groupstatement and proof · cited by 6,238
Subgroupstatement · cited by 3,593
MulActionstatement and proof · cited by 1,294
MulAction.stabilizerstatement and proof · cited by 254
SubMulActionstatement · cited by 120
MulAction.IsPretransitivestatement and proof · cited by 94
MulAction.IsMultiplyPretransitivestatement and proof · cited by 33
SubMulAction.ofStabilizerstatement and proof · cited by 33
MulAction.exists_smul_eqproof · cited by 32
SubMulAction.ofStabilizer.isMultiplyPretransitive_iff_of_conjproof · cited by 1

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