Normal subgroup of nilpotent group
This article describes a property that arises as the conjunction of a subgroup property: normal subgroup with a group property imposed on the ambient group: nilpotent group
View a complete list of such conjunctions | View a complete list of conjunctions where the group property is imposed on the subgroup
Definition
The term normal subgroup of nilpotent group is used for a subgroup of a group where the whole group is a nilpotent group and the subgroup is a normal subgroup.
Relation with other properties
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| subgroup of abelian group | ||||
| normal subgroup of group of prime power order | ||||
| characteristic subgroup of nilpotent group |
Weaker properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| normal subgroup | ||||
| normal subgroup contained in hypercenter | ||||
| subgroup of nilpotent group | ||||
| unipotent automorphism-invariant subgroup |