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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 Dempwolff group ： ウィキペディア英語版 Dempwolff group In mathematical finite group theory, the Dempwolff group is a finite group of order 319979520 = 215·32·5·7·31, that is the unique nonsplit extension $2^\backslash mathrm\_(\backslash mathbb\_)$ of $\backslash mathrm\_(\backslash mathbb\_)$ by its natural module of order $2^5$. The uniqueness of such a nonsplit extension was shown by , and the existence by , who showed using some computer calculations of that the Dempwolff group is contained in the compact Lie group $E\_$ as the subgroup fixing a certain lattice in the Lie algebra of $E\_$, and is also contained in the Thompson sporadic group (the full automorphism group of this lattice) as a maximal subgroup. showed that that any extension of $\backslash mathrm\_(\backslash mathbb\_)$ by its natural module $\backslash mathbb\_^$ splits if $q>2$, and showed that it also splits if $n$ is not 3, 4, or 5, and in each of these three cases there is just one non-split extension. These three nonsplit extensions can be constructed as follows: *The nonsplit extension $2^\backslash mathrm\_(\backslash mathbb\_)$ is a maximal subgroup of the Chevalley group $G\_(\backslash mathbb\_)$. *The nonsplit extension $2^\backslash mathrm\_(\backslash mathbb\_)$ is a maximal subgroup of the sporadic Conway group Co3. *The nonsplit extension $2^\backslash mathrm\_(\backslash mathbb\_)$ is a maximal subgroup of the Thompson sporadic group Th. ==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「Dempwolff 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.