论文标题
相对有限呈现的组的有限亚组
Bounded subgroups of relatively finitely presented groups
论文作者
论文摘要
考虑到有限生成的组$ g $，该$ g $相对于外围子组的集合而言相对有限，我们证明每个无限的亚组$ h $ $ g $的$ g $的$ g $中的$ g $的$ g $ bughate均与外围子组相结合。作为应用，我们获得了相对双曲基团的亚组的三分法。此外，我们证明了极限组的所有亚组的相对指数增长率的存在。
Given a finitely generated group $G$ that is relatively finitely presented with respect to a collection of peripheral subgroups, we prove that every infinite subgroup $H$ of $G$ that is bounded in the relative Cayley graph of $G$ is conjugate into a peripheral subgroup. As an application, we obtain a trichotomy for subgroups of relatively hyperbolic groups. Moreover we prove the existence of the relative exponential growth rate for all subgroups of limit groups.
