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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Transitively normal subgroup ： ウィキペディア英語版 Transitively normal subgroup 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, $H$ is a transitively normal subgroup of $G$ if for every $K$ normal in $H$, we have that $K$ is normal in $G$. 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 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.