Theorems · Theorem · group theory
Group.IsNilpotent.nilpotent
∀ (G : Type u_2) [inst : Group G] [Group.IsNilpotent G], ∃ n, Subgroup.upperCentralSeries G n = ⊤
- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 89 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement · cited by 9,680
- Groupstatement and proof · cited by 6,238
- Subgroupstatement · cited by 3,593
- Group.IsNilpotentstatement and proof · cited by 80
- Subgroup.upperCentralSeriesstatement · cited by 51
- Group.IsNilpotent.nilpotent'proof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- Group.nilpotencyClassproof · cited by 47
- Group.nilpotencyClass_defstatement · cited by 5
- Group.of_quotient_center_nilpotentproof · cited by 3
- Subgroup.upperCentralSeries_nilpotencyClassproof · cited by 3
- Group.nilpotencyClass_le_of_surjectiveproof · cited by 2
- Group.nilpotencyClass_zero_iff_subsingletonproof · cited by 2