Theorems · Theorem · group theory
AddGroup.nilpotencyClass_zero_iff_subsingleton
∀ {G : Type u_1} [inst : AddGroup G] [AddGroup.IsNilpotent G], AddGroup.nilpotencyClass G = 0 ↔ Subsingleton G- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 92 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topproof · cited by 9,680
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupproof · cited by 3,232
- AddGroup.IsNilpotentstatement and proof · cited by 42
- AddGroup.nilpotencyClassstatement · cited by 26
- subsingleton_iff_bot_eq_topproof · cited by 16
- Nat.find_eq_zeroproof · cited by 6
- AddGroup.IsNilpotent.nilpotentproof · cited by 5
- AddGroup.nilpotencyClass_defproof · cited by 5
- AddSubgroup.subsingleton_iffproof · cited by 3
- AddSubgroup.upperCentralSeries_zeroproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- AddGroup.nilpotencyClass_quotient_centerproof · cited by 2
- AddGroup.nilpotent_center_quotient_indproof · cited by 0