IsMultiplyPretransitive — Mathlib

English

The preprimitive property is equivalent under a natural equivalence of fixingSubgroups and their images.

Русский

Свойство предпримитивности эквивалентно через естественное соответствие фиксационных подгрупп и их образов.

LaTeX

$$IsPreprimitive (fixingSubgroup G s) (ofFixingSubgroup G s) ≃ IsPreprimitive (fixingSubgroup G (g • s)) (ofFixingSubgroup G (g • s))$$

Lean4

/-- An action of a group on a type `α` is `n`-pretransitive
if the associated action on `Fin n ↪ α` is pretransitive. -/
@[to_additive /-- An additive action of an additive group on a type `α`
    is `n`-pretransitive if the associated action on `Fin n ↪ α` is pretransitive. -/
    ]
abbrev IsMultiplyPretransitive (n : ℕ) :=
  IsPretransitive G (Fin n ↪ α)

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