Infinitely presented graphical small cancellation groups are acylindrically hyperbolic

Dominik Gruber, Alessandro Sisto

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)
28 Downloads (Pure)


We prove that infinitely presented graphical Gr(7) small cancellation groups are acylindrically hyperbolic. In particular, infinitely presented classical C(7)-groups and, hence, classical C′(1/6)-groups are acylindrically hyperbolic. We also prove the analogous statements for the larger class of graphical small cancellation presentations over free products. We construct infinitely presented classical C′(1/6)-groups that provide new examples of divergence functions of groups.

Original languageEnglish
Pages (from-to)2501-2552
Number of pages52
JournalAnnales de l'Institut Fourier
Issue number6
Early online date23 Nov 2018
Publication statusPublished - 2018


  • Acylindrical hyperbolicity
  • Divergence
  • Graphical small cancellation

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology


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