Central subgroup

In mathematics, in the field of group theory, a subgroup of a group is termed central if it lies inside the center of the group.
Given a group formula_1, the center of formula_1, denoted as formula_3, is defined as the set of those elements of the group which commute with every element of the group. The center is a characteristic subgroup. A subgroup formula_4 of formula_1 is termed "central" if formula_6.
Central subgroups have the following properties: