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.

, the center, 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 is termed central.

Central subgroups have the following properties:

• They are abelian groups (because, in particular, all elements of the center must commute with each other).

• They are normal subgroups. They are central factors, and are hence transitively normal subgroups.

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