Theorems · Definition · group theory
AddGroup.nilpotencyClass
(G : Type u_1) → [AddGroup G] → ℕ
The nilpotency class of a nilpotent additive 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
- 26 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
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.
- AddGroupstatement and proof · cited by 4,410
- Nat.findproof · cited by 139
- AddGroup.IsNilpotentproof · cited by 42
- AddGroup.IsNilpotent.nilpotentproof · cited by 5
Cited by27
Results whose statement or proof uses this declaration.
- AddSubgroup.lowerCentralSeries_eq_bot_iff_nilpotencyClass_lestatement and proof · cited by 5
- AddGroup.nilpotencyClass_defstatement · cited by 5
- AddSubgroup.upperCentralSeries_eq_top_iff_nilpotencyClass_lestatement and proof · cited by 4
- AddSubgroup.lowerCentralSeries_length_eq_nilpotencyClassstatement · cited by 4
- AddGroup.nilpotencyClass_of_not_nilpotentstatement · cited by 3
- AddGroup.nilpotencyClass_quotient_centerstatement and proof · cited by 2
- AddGroup.nilpotencyClass_zero_iff_subsingletonstatement · cited by 2
- AddSubgroup.upperCentralSeries_nilpotencyClassstatement · cited by 2
- AddSubgroup.lowerCentralSeries_nilpotencyClassstatement · cited by 2
- AddGroup.nilpotencyClass_le_of_ker_le_centerstatement and proof · cited by 1
- AddGroup.nilpotencyClass_le_of_surjectivestatement and proof · cited by 1
- AddSubgroup.least_ascending_central_series_length_eq_nilpotencyClassstatement · cited by 1