Norm (group)

From HandWiki

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