Quantifying separability in virtually special groups

Mark F. Hagen, Priyam Patel

Research output: Contribution to journalArticle (Academic Journal)peer-review

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We give a new, effective proof of the separability of cubically convex-cocompact subgroups of special groups. As a consequence, we show that if $G$ is a virtually compact special hyperbolic group, and $Q\leq G$ is a $K$-quasiconvex subgroup, then any $g\in G-Q$ of word-length at most $n$ is separated from $Q$ by a subgroup whose index is polynomial in $n$ and exponential in $K$. This generalizes a result of Bou-Rabee and the authors on residual finiteness growth and a result of the second author on surface groups.
Original languageEnglish
Pages (from-to)103-120
JournalPacific Journal of Mathematics
Issue number1
Publication statusPublished - 10 Jul 2016

Bibliographical note

12 pages, 5 figures. Revised in light of referee's comments. To appear in Pacific J. Math


  • math.GR
  • math.GT
  • 20E26, 20F36
  • subgroup separable
  • right-angled Artin groups
  • quantifying
  • virtually special groups

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