2-generator arithmetic Kleinian groups
2-generator arithmetic Kleinian groups
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2 生成元算术克莱因群
DOI：
10.1515/crll.1999.511.95
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发表时间：
1999
期刊：
影响因子：
--
通讯作者：
G. Martin
中科院分区：
文献类型：
--
作者：
C. Maclachlan;G. Martin
摘要 我们证明，在由有限阶两个元素生成的有限共体积克莱因群的无限多个共轭类中，只有有限多个算术共轭类。特别是算术广义三角形群的数量是有限的。后一个结果概括了竹内定理。
Abstract We show that among the infinitely many conjugacy classes of finite co-volume Kleinian groups generated by two elements of finite order, there are only finitely many which are arithmetic. In particular there are only finitely many arithmetic generalized triangle groups. This latter result generalizes a theorem of Takeuchi.