Characteristic central subgroup

Definition
A subgroup $$H$$ of a group $$G$$ is termed a characteristic central subgroup if it satisfies both these conditions:


 * 1) $$H$$ is a characteristic subgroup of $$G$$.
 * 2) $$H$$ is a central subgroup of $$G$$, i.e., it is contained in the center of $$G$$.