Theorems · Theorem · group theory

MulAction.is_one_pretransitive_iff

∀ {G : Type u_1} {α : Type u_2} [inst : Group G] [inst_1 : MulAction G α],
  MulAction.IsMultiplyPretransitive G α 1 ↔ MulAction.IsPretransitive G α

An action is 1-pretransitive iff it is pretransitive.

Defined in: Mathlib.GroupTheory.GroupAction.MultipleTransitivity
Cited by: 7 results in Mathlib
Foundations: Depth 30 from the axioms · uses propext, Quot.sound
Assumes: Group MulAction

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Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Groupstatement and proof · cited by 6,238
MulActionstatement and proof · cited by 1,294
MulAction.IsPretransitivestatement · cited by 94
MulAction.IsMultiplyPretransitivestatement · cited by 33
MulAction.oneEmbedding_isPretransitive_iffproof · cited by 1

Cited by7

Results whose statement or proof uses this declaration.

MulAction.IsMultiplyPretransitive.index_of_fixingSubgroup_mulproof · cited by 2
MulAction.IsPreprimitive.is_two_motive_of_is_motiveproof · cited by 2
MulAction.is_one_preprimitive_iffproof · cited by 2
alternatingGroup.isPretransitive_of_three_le_cardproof · cited by 2
MulAction.IsBlock.compl_subset_of_stabilizer_le_of_not_subset_of_not_subset_complproof · cited by 2
Set.powersetCard.isPretransitive_alternatingGroupproof · cited by 1
normalClosure_of_stabilizer_eq_topproof · cited by 0