Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strongly Quasiconvex subgroups in graphs of groups   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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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: gr-qc
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The categories of this paper are: cs
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom