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About: Norm (group)     Goto   Sponge   NotDistinct   Permalink

An Entity of Type : yago:Subgroup108001083, within Data Space : dbpedia.org associated with source document(s)

Type: yago:Abstraction100002137yago:Group100031264yago:WikicatFunctionalSubgroupsroad junctionyago:Subgroup108001083 New Facet based on Instances of this Class

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.