Rational embeddings of hyperbolic groups

James Belk*, Collin Bleak, Francesco Matucci

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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We prove that all Gromov hyperbolic groups embed into the asynchronous rational group defined by Grigorchuk, Nekrashevych and Sushchanskii. The proof involves assigning a system of binary addresses to points in the Gromov boundary of a hyperbolic group G, and proving that elements of G act on these addresses by asynchronous transducers. These addresses derive from a certain self-similar tree of subsets of G, whose boundary is naturally homeomorphic to the horofunction boundary of G.

Original languageEnglish
Pages (from-to)123-183
Number of pages61
JournalJournal of Combinatorial Algebra
Issue number2
Publication statusPublished - 15 Jun 2021


  • Hyperbolic groups
  • Rational group
  • Gromov boundary
  • Horofunction boundary
  • Transducers


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