Abstract The notions of stable and Morse subgroups of finitely generated groups generalize the concept of a quasiconvex subgroup of a word-hyperbolic group. For a word-hyperbolic group G, Kapovich [31] provided a partial algorithm which, on input a finite set S of G, halts if S generates a quasiconvex subgroup of G and runs forever otherwise. In this paper, we give various detection and decidability algorithms for stability and Morseness of a finitely generated subgroup of mapping class groups, right-angled Artin groups, toral relatively hyperbolic groups, and finitely generated groups discriminated by a locally quasiconvex torsion-free hyperbolic group (for example, ordinary limit groups).

中文翻译：

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检测有限生成群的稳定性和莫尔斯性的算法

摘要 有限生成群的稳定子群和莫尔斯子群的概念推广了词双曲群的拟凸子群的概念。对于词双曲群 G，Kapovich [31] 提供了一种部分算法，该算法在输入 G 的有限集 S 时，如果 S 生成 G 的拟凸子群，则停止，否则永远运行。在本文中，我们给出了各种检测和可判定性算法，用于映射类群的有限生成子群、直角 Artin 群、相对双曲群和由局部拟凸无扭双曲群区分的有限生成群的稳定性和莫尔斯性。 （例如，普通极限群）。