Theorems · Theorem · group theory
Subgroup.lowerCentralSeries_eq_bot_iff_nilpotencyClass_le
∀ {G : Type u_1} [inst : Group G] [hG : Group.IsNilpotent G] {n : ℕ},
⊤.lowerCentralSeries n = ⊥ ↔ Group.nilpotencyClass G ≤ n- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupGroup.IsNilpotent
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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 and proof · cited by 3,593
- eq_bot_iffproof · cited by 159
- Group.IsNilpotentstatement and proof · cited by 80
- Subgroup.lowerCentralSeriesstatement and proof · cited by 57
- Group.nilpotencyClassstatement and proof · cited by 47
- Nat.find_leproof · cited by 9
- Subgroup.lowerCentralSeries_length_eq_nilpotencyClassproof · cited by 5
- Subgroup.lowerCentralSeries_antitoneproof · cited by 3
- Subgroup.lowerCentralSeries_nilpotencyClassproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- Group.isNilpotent_pi_of_bounded_classproof · cited by 1
- Subgroup.lowerCentralSeries_eq_bot_iff_upperCentralSeries_eq_topproof · cited by 1
- lowerCentralSeries_eq_bot_iff_nilpotencyClass_leproof · cited by 0
- Subgroup.lowerCentralSeries_eq_bot_of_nilpotencyClass_leproof · cited by 0