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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 Margulis lemma ： ウィキペディア英語版 Margulis lemma In mathematics, the Margulis lemma (named after Grigory Margulis) is a result about discrete subgroups of isometries of a symmetric space (e.g. the hyperbolic n-space), or more generally a space of non-positive curvature. Theorem: Let S be a Riemannian symmetric space of non-compact type. There is a positive constant :$\backslash epsilon=\backslash epsilon(S)>0$ with the following property. Let F be a set of isometries of S. Suppose there is a point x in S such that : for all f in F. Assume further that the subgroup $\backslash Gamma$ generated by F is discrete in Isom(S). Then $\backslash Gamma$ is virtually nilpotent. More precisely, there exists a subgroup $\backslash Gamma\_0$ in $\backslash Gamma$ which is nilpotent of nilpotency class at most r and of index at most N in $\backslash Gamma$, where r and N are constants depending on S only. The constant $\backslash epsilon(S)$ is often referred as the ''Margulis constant''. ==References== *Werner Ballman, Mikhael Gromov, Victor Schroeder, ''Manifolds of Non-positive Curvature'', Birkhauser, Boston (1985) p. 107 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「Margulis lemma」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.