Groups with graphical C(6) and C(7) small cancellation presentations

TL;DR

This paper extends small cancellation theory to graphical presentations satisfying generalized C(6) and C(7) conditions, constructing lacunary hyperbolic groups and demonstrating the existence of non-abelian free subgroups.

Contribution

It generalizes classical small cancellation results to graphical settings and constructs new classes of hyperbolic groups with specific properties.

Findings

Construction of lacunary hyperbolic groups

Groups containing prescribed infinite sequences of graphs

Existence of non-abelian free subgroups in graphical C(7) groups

Abstract

We extend fundamental results of small cancellation theory to groups whose presentations satisfy the generalizations of the classical C(6) and C(7) conditions in graphical small cancellation theory. Using these graphical small cancellation conditions, we construct lacunary hyperbolic groups and groups that coarsely contain prescribed infinite sequences of finite graphs. We prove that groups given by (possibly infinite) graphical C(7) presentations contain non-abelian free subgroups.