Subgroup of nilpotent group

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This article describes a property that arises as the conjunction of a subgroup property: 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 subgroup of nilpotent group is used for a situation of a subgroup of a group where the whole group is a nilpotent group.

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 nilpotent group|FULL LIST, MORE INFO
normal subgroup of nilpotent group |FULL LIST, MORE INFO

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
hypernormalized subgroup |FULL LIST, MORE INFO
subnormal subgroup nilpotent implies every subgroup is subnormal Asymptotically fixed-depth join-transitively subnormal subgroup|FULL LIST, MORE INFO
subgroup of solvable group nilpotent implies solvable |FULL LIST, MORE INFO