Wise, Daniel T. Research announcement: The structure of groups with a quasiconvex hierarchy. (English) Zbl 1183.20043 Electron. Res. Announc. Math. Sci. 16, 44-55 (2009). 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. Cited in 6 ReviewsCited in 76 Documents 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 Keywords:word-hyperbolic groups; CAT(0) cube complexes; right-angled Artin groups; subgroup separable groups; 3-manifold groups; one-relator groups; subgroups of finite index; quasiconvex subgroups PDFBibTeX XMLCite \textit{D. T. Wise}, Electron. Res. Announc. Math. Sci. 16, 44--55 (2009; Zbl 1183.20043) Full Text: DOI