Norm (group)
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
- Baer, Reinhold. Der Kern, eine charakteristische Untergruppe, Compositio Mathematica 1: 254–283. Zbl9.15504
- Schmidt, Roland. Subgroup Lattices of Groups. de Gruyter, 1994
This article is issued from Wikipedia - version of the 4/6/2015. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.