Theorems · Theorem · group theory
AddGroup.of_quotient_center_nilpotent
∀ {G : Type u_1} [inst : AddGroup G], AddGroup.IsNilpotent (G ⧸ AddSubgroup.center G) → AddGroup.IsNilpotent GIf the quotient by center G is nilpotent, then so is G.
- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- AddSubgroupstatement · cited by 3,232
- HasQuotient.Quotientstatement and proof · cited by 2,301
- AddSubgroup.comapproof · cited by 123
- QuotientAddGroup.mk'proof · cited by 60
- AddGroup.IsNilpotentstatement and proof · cited by 42
- AddSubgroup.centerstatement and proof · cited by 40
- AddSubgroup.upperCentralSeriesproof · cited by 32
- AddSubgroup.comap_topproof · cited by 7
- AddGroup.IsNilpotent.nilpotentproof · cited by 5
- AddSubgroup.comap_upperCentralSeries_quotient_centerproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- AddGroup.nilpotencyClass_quotient_centerproof · cited by 2