中文摘要：

为研究实空间上光滑映射芽RL-等价关系下的相关问题,需要讨论光滑映射芽的RL有限决定性.讨论及计算了光滑映射芽在群RL-作用下的轨道切空间,得到了光滑映射芽的RL-有限决定的充分必要条件.

英文摘要：

In order to explore the relevant problems of smooth map germs under RL-equivalence, it is vital to discuss the RL-finite determinacy of smooth map germs. In this paper,the tangent space to orbit of smooth map germs under group =RL is calculated, and a necessary and sufficient condition with respect to RL-finite determinacy of smooth map germs is given.