Groups with graphical $C(6)$ and $C(7)$ small cancellation presentations
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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.References
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Additional Information
- Dominik Gruber
- Affiliation: Department of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria
- MR Author ID: 1089843
- Email: dominik.gruber@univie.ac.at
- 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 âANALYTICâ no. 259527.
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 3286508