Theorems · Theorem · group theory
Subgroup.mem_center_iff
∀ {G : Type u_1} [inst : Group G] {z : G}, z ∈ Subgroup.center G ↔ ∀ (g : G), g * z = z * g- Defined in
- Mathlib.GroupTheory.Subgroup.Center
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
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
- Subgroup.centerstatement and proof · cited by 121
- Semigroup.mem_center_iffproof · cited by 12
Cited by10
Results whose statement or proof uses this declaration.
- Subgroup.lowerCentralSeries_succ_eq_botproof · cited by 3
- alternatingGroup.center_eq_botproof · cited by 2
- Subgroup.upperCentralSeriesStep_eq_comap_centerproof · cited by 2
- Matrix.SpecialLinearGroup.mem_center_iffproof · cited by 2
- Matrix.GeneralLinearGroup.mem_center_iff_val_mem_range_scalarproof · cited by 2
- Matrix.SpecialLinearGroup.scalar_eq_self_of_mem_centerproof · cited by 2
- CommGroup.center_eq_topproof · cited by 1
- MonoidHom.isMulCommutative_of_isCyclic_of_ker_le_centerproof · cited by 1
- ConjClasses.mk_bijOnproof · cited by 1
- Subgroup.center_le_normalizerproof · cited by 1