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
[edit]- Baer, Reinhold (1934). "Der Kern, eine charakteristische Untergruppe". Compositio Mathematica. 1: 254–283.
- Schmidt, Roland (1994). Subgroup Lattices of Groups. Walter de Gruyter. ISBN 9783110112139.
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