Theorems · Definition · group theory

AddAction.block_stabilizerOrderIso

(G : Type u_1) →
  [inst : AddGroup G] →
    {X : Type u_2} →
      [inst_1 : AddAction G X] →
        [htGX : AddAction.IsPretransitive G X] →
          (a : X) → { B // a ∈ B ∧ AddAction.IsBlock G B } ≃o ↑(Set.Ici (AddAction.stabilizer G a))

Order equivalence between blocks in X containing a point a and subgroups of G containing the stabilizer of a (Wielandt, th. 7.5)

Defined in

Mathlib.GroupTheory.GroupAction.Blocks

Cited by

1 results in Mathlib

Foundations

Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddGroupAddActionAddAction.IsPretransitive