Theorems · Theorem · group theory
AddGroup.nilpotencyClass_def
∀ {G : Type u_1} [inst : AddGroup G] [hG : AddGroup.IsNilpotent G], AddGroup.nilpotencyClass G = Nat.find ⋯- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 91 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement · cited by 9,680
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- Nat.findstatement · cited by 139
- AddGroup.IsNilpotentstatement and proof · cited by 42
- AddSubgroup.upperCentralSeriesstatement · cited by 32
- AddGroup.nilpotencyClassstatement · cited by 26
- AddGroup.IsNilpotent.nilpotentstatement · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- AddSubgroup.upperCentralSeries_eq_top_iff_nilpotencyClass_leproof · cited by 4
- AddGroup.nilpotencyClass_zero_iff_subsingletonproof · cited by 2
- AddSubgroup.upperCentralSeries_nilpotencyClassproof · cited by 2
- AddGroup.nilpotencyClass_le_of_surjectiveproof · cited by 1
- AddSubgroup.least_ascending_central_series_length_eq_nilpotencyClassproof · cited by 1