Theorems · Theorem · group theory
AddSubgroup.mem_center_iff
∀ {G : Type u_1} [inst : AddGroup G] {z : G}, z ∈ AddSubgroup.center G ↔ ∀ (g : G), g + z = z + g- Defined in
- Mathlib.GroupTheory.Subgroup.Center
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
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.
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- AddSubgroup.centerstatement and proof · cited by 40
- AddSemigroup.mem_center_iffproof · cited by 9
Cited by7
Results whose statement or proof uses this declaration.
- AddSubgroup.center_eq_top_iffproof · cited by 3
- AddSubgroup.lowerCentralSeries_succ_eq_botproof · cited by 2
- AddMonoidHom.isAddCommutative_of_isAddCyclic_of_ker_le_centerproof · cited by 1
- AddSubgroup.upperCentralSeriesStep_eq_comap_centerproof · cited by 1
- AddCommGroup.center_eq_topproof · cited by 1
- QuotientAddGroup.comap_comap_centerproof · cited by 1
- AddSubgroup.center_le_normalizerproof · cited by 0