Theorems · Theorem · group theory
MulAction.IsBlock.orbit_stabilizer_eq
∀ {G : Type u_1} [inst : Group G] {X : Type u_2} [inst_1 : MulAction G X] {B : Set X} [MulAction.IsPretransitive G X],
MulAction.IsBlock G B → ∀ {a : X}, a ∈ B → MulAction.orbit (↥(MulAction.stabilizer G B)) a = BA 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 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Groupstatement and proof · cited by 6,238
- Subgroupstatement · cited by 3,593
- Set.extproof · cited by 2,266
- MulActionstatement and proof · cited by 1,294
- MulAction.stabilizerstatement and proof · cited by 254
- MulAction.orbitstatement and proof · cited by 114
- Set.mulActionSetstatement · cited by 95
- MulAction.IsPretransitivestatement and proof · cited by 94
- MulAction.IsBlockstatement and proof · cited by 73
- MulAction.exists_smul_eqproof · cited by 32
- Set.smul_mem_smul_set_iffproof · cited by 14
Cited by1
Results whose statement or proof uses this declaration.
- MulAction.IsBlock.ncard_block_eq_relIndexproof · cited by 1