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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 Metanilpotent group ： ウィキペディア英語版 Metanilpotent group In mathematics, in the field of group theory, a metanilpotent group is a group that is nilpotent by nilpotent. In other words, it has a normal nilpotent subgroup such that the quotient group is also nilpotent. In symbols, $G$ is metanilpotent if there is a normal subgroup $N$ such that both $N$ and $G/N$ are nilpotent. The following are clear: * Every metanilpotent group is a solvable group. * Every subgroup and every quotient of a metanilpotent group is metanilpotent. ==References== * J.C. Lennox, D.J.S. Robinson, ''The Theory of Infinite Soluble Groups'', Oxford University Press, 2004, ISBN 0-19-850728-3. P.27. * D.J.S. Robinson, ''A Course in the Theory of Groups'', GTM 80, Springer Verlag, 1996, ISBN 0-387-94461-3. P.150. 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「Metanilpotent group」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.