Theorems · Theorem · group theory
AddSubgroup.upperCentralSeries_eq_top_iff_nilpotencyClass_le
∀ {G : Type u_1} [inst : AddGroup G] [hG : AddGroup.IsNilpotent G] {n : ℕ},
AddSubgroup.upperCentralSeries G n = ⊤ ↔ AddGroup.nilpotencyClass G ≤ n- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroupAddGroup.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
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- eq_top_iffproof · cited by 236
- AddGroup.IsNilpotentstatement and proof · cited by 42
- AddSubgroup.upperCentralSeriesstatement and proof · cited by 32
- AddGroup.nilpotencyClassstatement and proof · cited by 26
- Nat.find_leproof · cited by 9
- AddGroup.nilpotencyClass_defproof · cited by 5
- AddSubgroup.upperCentralSeries_monoproof · cited by 3
- AddSubgroup.upperCentralSeries_nilpotencyClassproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- AddGroup.nilpotencyClass_quotient_centerproof · cited by 2
- AddSubgroup.lowerCentralSeries_eq_bot_iff_upperCentralSeries_eq_topproof · cited by 1
- AddCommGroup.nilpotencyClass_nonposproof · cited by 0
- AddGroup.IsNilpotent.nilpotencyClass_nonpos_iffproof · cited by 0