Center (algebra)

In general, the center of an algebraic structure is the set of elements which commute with every of the structure. With groups, this definition is straightforward; for rings and fields, the commutativity in question is multiplicative commutativity.

The center of a group is never empty, as the identity commutes with every element of a group. The center of a group is a subgroup of the group—a normal subgroup, in fact; it is also stable under any endomorphism on the group.

See also

• Centralizer

This article is a stub. Help us out by expanding it.