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Research announcement: The structure of groups with a quasiconvex hierarchy. (English) Zbl 1183.20043

Summary: Let \(G\) be a word-hyperbolic group with a quasiconvex hierarchy. We show that \(G\) has a finite index subgroup \(G'\) that embeds as a quasiconvex subgroup of a right-angled Artin group. It follows that every quasiconvex subgroup of \(G\) is a virtual retract, and is hence separable. The results are applied to certain 3-manifold and one-relator groups.

MSC:

20F67 Hyperbolic groups and nonpositively curved groups
20E07 Subgroup theorems; subgroup growth
20F36 Braid groups; Artin groups
20E26 Residual properties and generalizations; residually finite groups
20F05 Generators, relations, and presentations of groups
57M07 Topological methods in group theory
20F65 Geometric group theory
53C23 Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
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