Theorems · Theorem · group theory

MulAction.IsBlock.subsingleton_of_card_lt

∀ {G : Type u_1} [inst : Group G] {X : Type u_2} [inst_1 : MulAction G X] [MulAction.IsPretransitive G X] {B : Set X}
  [Finite X], MulAction.IsBlock G B → Nat.card X < 2 * (MulAction.orbit G B).ncard → B.Subsingleton

If a block has too many translates, then it is a (sub)singleton

Defined in

Mathlib.GroupTheory.GroupAction.Blocks

Cited by

0 results in Mathlib

Foundations

Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupMulActionMulAction.IsPretransitiveFinite