Infinitely presented graphical small cancellation groups are acylindrically hyperbolic
Abstract
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 $C'(\frac{1}{6})$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 $C'(\frac{1}{6})$groups that provide new examples of divergence functions of groups.
 Publication:

arXiv eprints
 Pub Date:
 August 2014
 DOI:
 10.48550/arXiv.1408.4488
 arXiv:
 arXiv:1408.4488
 Bibcode:
 2014arXiv1408.4488G
 Keywords:

 Mathematics  Group Theory;
 20F06 (Primary);
 20F65;
 20F67 (Secondary)
 EPrint:
 32 pages, 11 figures, v2: added references, v3: expanded proofs, improved exposition, reorganized subsections