Group Theory
Group Theory
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DOI：
10.1142/9789814304979_0002
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发表时间：
2019-08
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通讯作者：
Sudesh Shah Asha Shankar
中科院分区：
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作者：
Sudesh Shah Asha Shankar
我们研究李群中具有有限个连通分支的格的有限扩张群。我们证明了每一个非余紧Fuchsian群（这些是PSL（2，R）中的非余紧格）都有一个有限指数的扩张群，它不同构于具有有限个连通分支的李群中的格。另一方面，我们证明，在适当的意义上，这些是李群中唯一具有此类扩张群的格。我们还证明了具有有限个连通分支的李群中的格的有限个指数的扩张群只有有限个共轭类的有限个子群。引用这篇文章：F。格鲁内瓦尔德，V. Platonov，C. R. Acad. Sci.巴黎，系列I 338（2004年）。
We study finite extension groups of lattices in Lie groups which have finitely many connected components. We show that every non-cocompact Fuchsian group (these are the non-cocompact lattices in PSL ( 2 , R ) ) has an extension group of finite index which is not isomorphic to a lattice in a Lie group with finitely many connected components. On the other hand we prove that these are, in an appropriate sense, the only lattices in Lie groups which have extension groups of this kind. We also show that an extension group of finite index of a lattice in a Lie group with finitely many connected components has only finitely many conjugacy classes of finite subgroups. To cite this article: F. Grunewald, V. Platonov, C. R. Acad. Sci. Paris, Ser. I 338 (2004).