Theorems · Theorem · group theory

MulAction.IsBlock.of_subset

∀ {G : Type u_1} [inst : Group G] {X : Type u_2} [inst_1 : MulAction G X] [MulAction.IsPretransitive G X] {B : Set X}
  (a : X), B.Finite → MulAction.IsBlock G (⋂ k, ⋂ (_ : a ∈ k • B), k • B)

The intersection of the translates of a finite subset which contain a given point is a block (Wielandt, th. 7.3).

Defined in

Mathlib.GroupTheory.GroupAction.Blocks

Cited by

1 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupMulActionMulAction.IsPretransitive