Theorems · Theorem · group theory

AddAction.isMultiplyPreprimitive_succ_iff_ofStabilizer

∀ (M : Type u_1) (α : Type u_2) [inst : AddGroup M] [inst_1 : AddAction M α] [AddAction.IsPretransitive M α] {n : ℕ},
  1 ≤ n →
    ∀ {a : α},
      AddAction.IsMultiplyPreprimitive M α n.succ ↔
        AddAction.IsMultiplyPreprimitive (↥(AddAction.stabilizer M a)) (↥(SubAddAction.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: 0 results in Mathlib
Foundations: Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AddGroup AddAction AddAction.IsPretransitive

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