Theorems · Theorem · group theory

AddAction.IsBlock.orbit_stabilizer_eq

∀ {G : Type u_1} [inst : AddGroup G] {X : Type u_2} [inst_1 : AddAction G X] {B : Set X}
  [AddAction.IsPretransitive G X],
  AddAction.IsBlock G B → ∀ {a : X}, a ∈ B → AddAction.orbit (↥(AddAction.stabilizer G B)) a = B

A block containing a is the orbit of a under its stabilizer

Defined in

Mathlib.GroupTheory.GroupAction.Blocks

Cited by

1 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddGroupAddActionAddAction.IsPretransitive