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arXiv · 2204.09242

Strongly Quasiconvex subgroups in graphs of groups

Hoang Thanh Nguyen·Hung Cong Tran
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Abstract

Given a graph of groups $\mathcal{G} = (\Gamma, \{G_v\}, \{G_e\})$ 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.

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Hoang Thanh Nguyen, Hung Cong Tran. 2022-04-20. Strongly Quasiconvex subgroups in graphs of groups. https://arxiv.org/abs/2204.09242

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