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