Theorems · Theorem · group theory
Subgroup.upperCentralSeries_eq_top_iff_nilpotencyClass_le
∀ {G : Type u_1} [inst : Group G] [hG : Group.IsNilpotent G] {n : ℕ},
Subgroup.upperCentralSeries G n = ⊤ ↔ Group.nilpotencyClass G ≤ n- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 93 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.
Cites11
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
- eq_top_iffproof · cited by 236
- Group.IsNilpotentstatement and proof · cited by 80
- Subgroup.upperCentralSeriesstatement and proof · cited by 51
- Group.nilpotencyClassstatement and proof · cited by 47
- Nat.find_leproof · cited by 9
- Group.nilpotencyClass_defproof · cited by 5
- Subgroup.upperCentralSeries_monoproof · cited by 5
- Subgroup.upperCentralSeries_nilpotencyClassproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- Group.nilpotencyClass_quotient_centerproof · cited by 3
- Subgroup.lowerCentralSeries_eq_bot_iff_upperCentralSeries_eq_topproof · cited by 1
- CommGroup.nilpotencyClass_le_oneproof · cited by 1
- Group.IsNilpotent.nilpotencyClass_le_one_iffproof · cited by 0
- upperCentralSeries_eq_top_iff_nilpotencyClass_leproof · cited by 0