Theorems · Theorem · group theory

MulAction.isMultiplyPreprimitive_succ_iff_ofStabilizer

∀ (M : Type u_1) (α : Type u_2) [inst : Group M] [inst_1 : MulAction M α] [MulAction.IsPretransitive M α] {n : ℕ},
  1 ≤ n →
    ∀ {a : α},
      MulAction.IsMultiplyPreprimitive M α n.succ ↔
        MulAction.IsMultiplyPreprimitive (↥(MulAction.stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n

A pretransitive action is n.succ-preprimitive iff the action of stabilizers is n-preprimitive.

Defined in: Mathlib.GroupTheory.GroupAction.MultiplePrimitivity
Cited by: 2 results in Mathlib
Foundations: Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Group MulAction MulAction.IsPretransitive

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

Setproof · cited by 53,352
Groupstatement and proof · cited by 6,238
Set.imageproof · cited by 5,609
ENatproof · cited by 4,985
Set.preimageproof · cited by 4,946
Subgroupstatement · cited by 3,593
Nat.cast_oneproof · cited by 2,501
zero_addproof · cited by 2,366
Set.extproof · cited by 2,266
MulActionstatement and proof · cited by 1,294
Nat.cast_addproof · cited by 586
Set.encardproof · cited by 327

Cited by2

Results whose statement or proof uses this declaration.

MulAction.IsPreprimitive.is_two_motive_of_is_motiveproof · cited by 2
MulAction.IsPreprimitive.isMultiplyPreprimitiveproof · cited by 2