Theorems · Definition · group theory
commGroupOfNilpotencyClass
{G : Type u_1} → [inst : Group G] → [Group.IsNilpotent G] → Group.nilpotencyClass G ≤ 1 → CommGroup GGroups with nilpotency class at most one are abelian.
- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 95 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- CommGroupstatement · cited by 990
- Group.IsNilpotentstatement and proof · cited by 80
- Group.nilpotencyClassstatement and proof · cited by 47
- Group.commGroupOfCenterEqTopproof · cited by 0
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.