Theorems · Theorem · group theory

MulAction.IsBlock.ncard_block_mul_ncard_orbit_eq

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

The cardinality of the ambient space is the product of the cardinality of a block by the cardinality of the set of translates of that block

Defined in

Mathlib.GroupTheory.GroupAction.Blocks

Cited by

4 results in Mathlib

Foundations

Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupMulActionMulAction.IsPretransitive