论文标题
在组图中强烈的Quasiconvex亚组
Strongly Quasiconvex subgroups in graphs of groups
论文作者
论文摘要
给定$ \ Mathcal {g} =（γ，\ {g_v \}，\ {g_e \}）$的$ \ nathcal {g} =（γ，\ {g_v \}）$，具有某些条件上的有顶点组，$ g $在其贝斯 - 塞雷树$ t $上均在其贝斯 - serre $ t上。令$ h $为有限生成的$ g $的子组。我们证明了以下声明等价：$ h $具有有限的高度，$（g，t，h）$是$ a/qi $ - 三重，$ h $是Quasiconvex的，并且在$ g $中几乎是免费的。我们还提供了一个条件，以确定在合并下是否保留了一组中强的准清理性。
Given a graph of groups $\mathcal{G} = (Γ, \{G_v\}, \{G_e\})$ with certain conditions on vertex groups and $G$ acts acylindrically on its Bass-Serre tree $T$. Let $H$ be a finitely generated subgroup of $G$. We prove the following statements equivalence: $H$ has finite height, $(G, T, H)$ is a $A/QI$--triple, $H$ is strongly quasiconvex and virtually free in $G$. We also give a condition to determine whether strong quasiconvexity in a group is preserved under amalgams.
