Research announcement: The structure of groups with a quasiconvex hierarchy

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January 2009, 16: 44-55. doi: 10.3934/era.2009.16.44

Research announcement: The structure of groups with a quasiconvex hierarchy

1.	Dept. of Math. & Stats., McGill University, Montreal, QC, Canada

Received August 2009 Revised September 2009 Published October 2009

Abstract
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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.

Keywords: CAT(0) cube complex, right-angled artin group, 3-manifold, subgroup separable, one-relator group..

Mathematics Subject Classification: 53C23, 20F36, 20F55, 20F67, 20F65, 20E2.

Citation: Daniel T. Wise. Research announcement: The structure of groups with a quasiconvex hierarchy. Electronic Research Announcements, 2009, 16: 44-55. doi: 10.3934/era.2009.16.44

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