Nilpotent quotient-by-core subgroup

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Definition

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 $H$ ).