In mathematics, in the field of group theory, the norm of a group is the intersection of the normalizers of all its subgroups. This is also termed the Baer norm, after Reinhold Baer. The following facts are true for the Baer norm: It is a characteristic subgroup. It contains the center of the group. It is contained inside the second term of the upper central series. It is a Dedekind group, so is either abelian or has a direct factor isomorphic to the quaternion group. If it contains an element of infinite order, then it is equal to the center of the group. References Group theory Functional subgroups