Theorems · Definition · group theory
Group.nilpotencyClass
(G : Type u_1) → [Group G] → ℕ
The nilpotency class of a nilpotent group is the smallest natural n such that
the n-th term of the upper central series is G. If G is not nilpotent then the nilpotency
class takes the junk value 0.
- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 47 results in Mathlib
- Foundations
- Depth 90 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.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- Nat.findproof · cited by 139
- Group.IsNilpotentproof · cited by 80
- Group.IsNilpotent.nilpotentproof · cited by 5
Cited by48
Results whose statement or proof uses this declaration.
- Group.nilpotencyClass_defstatement · cited by 5
- Subgroup.upperCentralSeries_eq_top_iff_nilpotencyClass_lestatement and proof · cited by 5
- Subgroup.lowerCentralSeries_length_eq_nilpotencyClassstatement · cited by 5
- Subgroup.lowerCentralSeries_eq_bot_iff_nilpotencyClass_lestatement and proof · cited by 4
- Group.nilpotencyClass_of_not_nilpotentstatement · cited by 3
- Group.nilpotencyClass_quotient_centerstatement and proof · cited by 3
- Subgroup.upperCentralSeries_nilpotencyClassstatement · cited by 3
- Subgroup.lowerCentralSeries_nilpotencyClassstatement · cited by 3
- Subgroup.upperCentralSeries.StrictMonoOnstatement and proof · cited by 2
- Group.nilpotencyClass_le_of_ker_le_centerstatement and proof · cited by 2
- Group.nilpotencyClass_le_of_surjectivestatement and proof · cited by 2
- Group.nilpotencyClass_zero_iff_subsingletonstatement · cited by 2