Theorems · Theorem · group theory
Subgroup.lowerCentralSeries_eq_bot_iff_upperCentralSeries_eq_top
∀ {G : Type u_1} [inst : Group G] {n : ℕ}, ⊤.lowerCentralSeries n = ⊥ ↔ Subgroup.upperCentralSeries G n = ⊤- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 99 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.
Cites10
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
- Bot.botstatement and proof · cited by 4,720
- Subgroupstatement · cited by 3,593
- Group.IsNilpotentproof · cited by 80
- Subgroup.lowerCentralSeriesstatement and proof · cited by 57
- Subgroup.upperCentralSeriesstatement and proof · cited by 51
- Subgroup.nilpotent_iff_lowerCentralSeriesproof · cited by 9
- Subgroup.upperCentralSeries_eq_top_iff_nilpotencyClass_leproof · cited by 5
- Subgroup.lowerCentralSeries_eq_bot_iff_nilpotencyClass_leproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.lowerCentralSeries_one_eq_bot_iffproof · cited by 0