Nilpotent quotient-by-core subgroup

Symbol-free definition
A subgroup of a group is said to be nilpotent quotient-by-core if the quotient-by-core of this subgroup (that is, its quotient by its normal core) is a nilpotent group.

Definition with symbols
A subgroup $$H$$ in a group $$G$$ is termed nilpotent quotient-by-core if $$H/H_G$$ is a nilpotent group where $$H_G$$ denotes the normal core of $$H$$ (or the intersection of conjugates of $$H$$).

Stronger properties

 * Normal subgroup
 * Permutable subgroup (when we are working with finite groups)
 * Modular subgroup (when we are working with finite groups)