The double of a virtually compact special Gromov-hyperbolic group along a quasiconvex subgroup is virtually compact special, with a generalization to certain graphs of groups.
Stature and separability in graphs of groups
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abstract
We introduce the notion of finite stature of a family $\{H_i\}$ of subgroups of a group $G$. We investigate the separability of subgroups of a group $G$ that splits as a graph of hyperbolic special groups with quasiconvex edge groups. We prove that when the vertex groups of $G$ have finite stature, then quasiconvex subgroups of the vertex groups of $G$ are separable in $G$. We present some partial results in a relatively hyperbolic framework.
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math.GR 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Virtual specialness of the double
The double of a virtually compact special Gromov-hyperbolic group along a quasiconvex subgroup is virtually compact special, with a generalization to certain graphs of groups.