Theorems · Theorem · group theory
Subgroup.upperCentralSeries_one_eq_top_iff
∀ {G : Type u_1} [inst : Group G], Subgroup.upperCentralSeries G 1 = ⊤ ↔ IsMulCommutative G- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 91 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- IsMulCommutativestatement and proof · cited by 95
- Subgroup.upperCentralSeriesstatement · cited by 51
- Subgroup.upperCentralSeries_oneproof · cited by 7
- Subgroup.center_eq_top_iffproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Subgroup.lowerCentralSeries_one_eq_bot_iffproof · cited by 0
- Group.IsNilpotent.nilpotencyClass_le_one_iffproof · cited by 0