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# Research announcement: The structure of groups with a quasiconvex hierarchy

• 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.
Mathematics Subject Classification: 53C23, 20F36, 20F55, 20F67, 20F65, 20E26.

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