Theorems · Theorem · group theory
Subgroup.least_ascending_central_series_length_eq_nilpotencyClass
∀ {G : Type u_1} [inst : Group G] [hG : Group.IsNilpotent G], Nat.find ⋯ = Group.nilpotencyClass GThe nilpotency class of a nilpotent G is equal to the smallest n for which an ascending
central series reaches G in its n-th term.
- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 92 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.
Cites15
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
- le_antisymmproof · cited by 2,068
- top_le_iffproof · cited by 175
- Nat.findstatement and proof · cited by 139
- Group.IsNilpotentstatement and proof · cited by 80
- Subgroup.upperCentralSeriesproof · cited by 51
- Group.nilpotencyClassstatement · cited by 47
- Subgroup.IsAscendingCentralSeriesstatement and proof · cited by 14
- Nat.find_monoproof · cited by 10
- Group.nilpotencyClass_defproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- Subgroup.least_descending_central_series_length_eq_nilpotencyClassproof · cited by 2
- least_ascending_central_series_length_eq_nilpotencyClassproof · cited by 0