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In mathematics, in the field of group theory, a subgroup of a group is termed malnormal if for any in but not in , and intersect in the identity element.〔.〕 Some facts about malnormality: *An intersection of malnormal subgroups is malnormal.〔.〕 *Malnormality is transitive, that is, a malnormal subgroup of a malnormal subgroup is malnormal.〔.〕 *The trivial subgroup and the whole group are malnormal subgroups. A normal subgroup that is also malnormal must be one of these.〔.〕 *Every malnormal subgroup is a special type of C-group called a trivial intersection subgroup or TI subgroup. When ''G'' is finite, a malnormal subgroup ''H'' distinct from 1 and ''G'' is called a "Frobenius complement".〔 The set ''N'' of elements of ''G'' which are, either equal to 1, or non-conjugate to any element of ''G'', is a normal subgroup of ''G'', called the "Frobenius kernel", and ''G'' is the semi-direct product of ''H'' and ''N'' (Frobenius' theorem).〔.〕 ==References== 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「Malnormal subgroup」の詳細全文を読む スポンサード リンク
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