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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: 254283. (Zbl9.15504 ) * Schmidt, Roland. Subgroup Lattices of Groups. de Gruyter, 1994 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Norm (group)」の詳細全文を読む スポンサード リンク
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