is_two_pretransitive — Mathlib

English

Under a preprimitive hypothesis, for subsets with |s| = n+1 and large α, IsMultiplyPreprimitive G α (n+2) holds provided a suitable hypothesis on the fixingSubgroup holds.

Русский

При предположении пред primitive, для подмножеств с |s| = n+1 и большими α выполняется IsMultiplyPreprimitive G α (n+2) при подходящем условии относительно fixingSubgroup.

LaTeX

$$IsMultiplyPreprimitive G α (n+2)$$

Lean4

/-- A criterion due to Jordan for being 2-pretransitive (Wielandt, 13.1) -/
theorem is_two_pretransitive (hG : IsPreprimitive G α) {s : Set α} {n : ℕ} (hsn : s.ncard = n + 1)
    (hsn' : n + 2 < Nat.card α) (hs_trans : IsPretransitive (fixingSubgroup G s) (SubMulAction.ofFixingSubgroup G s)) :
    IsMultiplyPretransitive G α 2 :=
  (hG.is_two_motive_of_is_motive hsn hsn').1 hs_trans

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