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 ≤ Z ( G ) .
Central subgroups have the following properties:
They are abelian groups.They are normal subgroups. They are central factors, and are hence transitively normal subgroups.