Theorems · Theorem · group theory
CommGroup.nilpotencyClass_le_one
∀ {G : Type u_2} [inst : CommGroup G], Group.nilpotencyClass G ≤ 1Abelian groups have nilpotency class at most one.
- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topproof · cited by 9,680
- Subgroupproof · cited by 3,593
- CommGroupstatement and proof · cited by 990
- Group.nilpotencyClassstatement · cited by 47
- Subgroup.upperCentralSeries_oneproof · cited by 7
- Subgroup.upperCentralSeries_eq_top_iff_nilpotencyClass_leproof · cited by 5
- CommGroup.center_eq_topproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Group.nilpotencyClass_le_one_of_isSimple_of_isNilpotentproof · cited by 1