Theorems · Theorem · group theory

MulAction.IsBlock.stabilizer_le

∀ {G : Type u_1} [inst : Group G] {X : Type u_2} [inst_1 : MulAction G X] {B : Set X},
  MulAction.IsBlock G B → ∀ {a : X}, a ∈ B → MulAction.stabilizer G a ≤ MulAction.stabilizer G B

If B is a block containing a, then the stabilizer of B contains the stabilizer of a

Defined in

Mathlib.GroupTheory.GroupAction.Blocks

Cited by

1 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupMulAction