Groups with graphical C(6) and C(7) small cancellation presentations
Group Theory
2014-07-25 v2
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.
Keywords
Cite
@article{arxiv.1210.0178,
title = {Groups with graphical C(6) and C(7) small cancellation presentations},
author = {Dominik Gruber},
journal= {arXiv preprint arXiv:1210.0178},
year = {2014}
}
Comments
32 pages, 6 figures. Minor improvements in exposition, added Theorem 3.4. Trans. Amer. Math. Soc., in press