Packing subgroups in relatively hyperbolic groups

By G. Hruska, Daniel T Wise, Christopher Hruska. 2006

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Our main result establishes the bounded packing of relatively quasiconvex subgroups of a relatively hyperbolic group, under mild hypotheses. As an application, we prove that relatively quasiconvex subgroups have finite height and width, properties that strongly restrict the way families of distinct conjugates of the subgroup can intersect. We prove that an infinite, nonparabolic relatively quasiconvex subgroup of a relatively hyperbolic group has finite index in its commensurator. We also prove a virtual malnormality theorem for separable, relatively quasiconvex subgroups, which is new even in the word hyperbolic case. 20F65; 20F67, 20F69

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/145a6f47aee2002e8cb93ea3e5529ad7826959b2

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Quasiconvexity and relatively hyperbolic groups that split (2012, background): “n the Bass-Serre tree. Then H is relativelyquasiconvex in G. When the edge groups are separable in G, there is a ﬁnite index subgroup G′ whose splitting has relatively malnormal edge groups (see e.g. [11, 9]). Consequently, if moreover, the edge groups of G are total, then the induced splitting of G”
On strongly quasiconvex subgroups (2017, background): “allenging. In [AMST], Antol´ın-Mj-Sisto-Taylor prove that if K = {K1,··· ,Kℓ} is a ﬁnite collection of stable subgroups of a ﬁnitely generated group G, then K has bounded packing and ﬁnite width (see [HW09] for packing subgroups and [GMRS98] for widths of subgroups). However, it seems diﬃcult to gen”