Infinitely presented graphical small cancellation groups are\n acylindrically hyperbolic

2014/08/19 by Dominik Gruber, Alessandro Sisto, Gruber, Dominik +1 · 2 citations
Computer Science · Mathematics · #20F06 (Primary) #20F65 #20F67 (Secondary) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1408.4488

openalex publication_date 2014/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that infinitely presented graphical Gr(7) small cancellation\ngroups are acylindrically hyperbolic. In particular, infinitely presented\nclassical C(7)-groups and, hence, classical C'(\(1)/(6))-groups are\nacylindrically hyperbolic. We also prove the analogous statements for the\nlarger class of graphical small cancellation presentations over free products.\nWe construct infinitely presented classical C'(\(1)/(6))-groups that\nprovide new examples of divergence functions of groups.\n

Cited by

• The CLT for lamplighter groups with an acylindrically hyperbolic base
• Graphical small cancellation and hyperfiniteness of boundary actions

Related

• Groups with graphical C(6) and C(7) small cancellation presentations
• Small cancellation in acylindrically hyperbolic groups
• Relative Hyperbolicity of Graphical Small Cancellation Groups
• Groups acting acylindrically on hyperbolic spaces
• Infinitely presented small cancellation groups have the Haagerup property