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, the center of, denoted as, 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 of is termed central if.
Central subgroups have the following properties:

They are abelian groups.
They are normal subgroups. They are central factors, and are hence transitively normal subgroups.