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arxiv: 1210.0178 · v2 · pith:G757DKQLnew · submitted 2012-09-30 · 🧮 math.GR

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

Dominik Gruber This is my paper
classification 🧮 math.GR
keywords groupscancellationgraphicalsmallpresentationsconditionscontaininfinite
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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.

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