Theorems · Theorem · group theory
MulAction.mem_stabilizer_iff
∀ {G : Type u_1} {α : Type u_2} [inst : Group G] [inst_1 : MulAction G α] {a : α} {g : G},
g ∈ MulAction.stabilizer G a ↔ g • a = a- Defined in
- Mathlib.GroupTheory.GroupAction.Defs
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- Subgroupstatement · cited by 3,593
- MulActionstatement and proof · cited by 1,294
- MulAction.stabilizerstatement · cited by 254
Cited by20
Results whose statement or proof uses this declaration.
- stabilizer_complproof · cited by 7
- MulAction.stabilizer_mul_selfproof · cited by 3
- alternatingGroup.stabilizer.surjective_toPermproof · cited by 2
- Equiv.Perm.ofSubtype_mem_stabilizerproof · cited by 2
- Equiv.Perm.swap_mem_stabilizerproof · cited by 2
- MulAction.mem_stabilizer_finset_iff_subset_smul_finsetproof · cited by 2
- MulAction.IsBlock.of_subsetproof · cited by 1
- MulAction.fixingSubgroup_le_stabilizerproof · cited by 1
- MulAction.le_stabilizer_iff_smul_leproof · cited by 1
- Equiv.Perm.stabilizer_ne_top_of_nonempty_of_nonempty_complproof · cited by 1
- MulAction.mem_stabilizer_setproof · cited by 1
- CategoryTheory.PreGaloisCategory.stabilizer_normal_of_isGaloisproof · cited by 1