Theorems · Theorem · group theory
Subgroup.isNilpotent_of_ker_le_center
∀ {G : Type u_1} [inst : Group G] {H : Type u_2} [inst_1 : Group H] (f : G →* H),
f.ker ≤ Subgroup.center G → ∀ [Group.IsNilpotent H], Group.IsNilpotent GThe preimage of a nilpotent group is nilpotent if the kernel of the homomorphism is contained in the center.
- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupGroupGroup.IsNilpotent
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topproof · cited by 9,680
- Groupstatement and proof · cited by 6,238
- Bot.botproof · cited by 4,720
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement and proof · cited by 3,593
- le_transproof · cited by 985
- le_topproof · cited by 411
- Subgroup.mapproof · cited by 301
- MonoidHom.kerstatement and proof · cited by 212
- Subgroup.centerstatement and proof · cited by 121
- le_bot_iffproof · cited by 116
- Group.IsNilpotentstatement and proof · cited by 80
Cited by2
Results whose statement or proof uses this declaration.
- Group.nilpotencyClass_le_of_ker_le_centerproof · cited by 2
- isNilpotent_of_ker_le_centerproof · cited by 0