Differential coding

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 $G$, the center of $G$, denoted as $Z(G)$, 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 and is also an abelian group (because, in particular, all elements of the center must commute with each other). A subgroup $H$ of $G$ is termed central if $H\le Z(G)$.

Central subgroups have the following properties:

• They are abelian groups.
• They are normal subgroups. In fact, they are central factors, and are hence transitively normal subgroups.

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