This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]
A subgroup of a group is termed a nilpotent-quotient subgroup or nilpotent-quotient normal subgroup if it is a normal subgroup and the quotient group is a nilpotent group.
Relation with other properties
The intersection of all nilpotent-quotient normal subgroups is termed the nilpotent residual, and this is also described as the term of the transfinite lower central series It is trivial if and only if the group is a residually nilpotent group. In a finite group, the nilpotent residual is itself a nilpotent-quotient normal subgroup.