In this paper, we consider the conjugacy stability property of subgroups and provide effective procedures to solve the problem in several classes of groups. In particular, we start with free groups, that is, we give an effective procedure to find out if a finitely generated subgroup of a free group is conjugacy stable. Then we further generalize this result to quasi-convex subgroups of torsion-free hyperbolic groups and finitely generated subgroups of limit groups.

中文翻译：

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检测某些类群中子群的共轭稳定性

在本文中，我们考虑了子群的共轭稳定性特性，并提供了解决几类群中问题的有效程序。特别地，我们从自由群开始，也就是说，我们给出了一个有效的程序来找出一个自由群的有限生成子群是否是共轭稳定的。然后我们进一步将这个结果推广到无扭双曲群的拟凸子群和极限群的有限生成子群。