关于代数有限型Klein群

ON KLEINIAN GROUPS OF ALGEBRAIC FINITE TYPE

本文推广了Ａｈｌｆｏｒｓ关于Ｋｌｅｉｎ群的著名定理，在Ｋｌｅｉｎ群的研究中引进代数有限型的概念，证明Ｋｌｅｉｎ群是代数有限型的，当且仅当它是分析有限型的，从而给出Ｋｌｅｉｎ群有限性的一个代数判据。

In this paper,the concept of algebraic finite type is introduced in the research of kleinian groups.It is proved that a kleinian group is of algebraic finite type if and only if it is of analytic finite type,which generalizes the famous theorem of Ahlfors' finiteness and gives an algebraic data for the finiteness of kleinian groups.