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


Author: Dominik Gruber
Journal: Trans. Amer. Math. Soc. 367 (2015), 2051-2078
MSC (2010): Primary 20F06; Secondary 20F65, 20F67
DOI: https://doi.org/10.1090/S0002-9947-2014-06198-9
Published electronically: July 29, 2014
MathSciNet review: 3286508
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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.


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Additional Information

Dominik Gruber
Affiliation: Department of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria
Email: dominik.gruber@univie.ac.at

DOI: https://doi.org/10.1090/S0002-9947-2014-06198-9
Keywords: Small cancellation theory
Received by editor(s): October 16, 2012
Received by editor(s) in revised form: May 1, 2013, and May 19, 2013
Published electronically: July 29, 2014
Additional Notes: This work was supported by the ERC grant of Professor Goulnara Arzhantseva “ANALYTIC” no. 259527.
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.