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In mathematics, in the field of group theory, a subgroup of a group is said to be transitively normal in the group if every normal subgroup of the subgroup is also normal in the whole group. In symbols, is a transitively normal subgroup of if for every normal in , we have that is normal in . An alternate way to characterize these subgroups is: every ''normal subgroup preserving automorphism'' of the whole group must restrict to a ''normal subgroup preserving automorphism'' of the subgroup. Here are some facts about transitively normal subgroups: *Every normal subgroup of a transitively normal subgroup is normal. *Every direct factor, or more generally, every central factor is transitively normal. Thus, every central subgroup is transitively normal. *A transitively normal subgroup of a transitively normal subgroup is transitively normal. *A transitively normal subgroup is normal. == See also == * Normal subgroup 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「transitively normal subgroup」の詳細全文を読む スポンサード リンク
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