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Mathematical Notes

, Volume 103, Issue 3–4, pp 610–615 | Cite as

An Approach to the Study of Finitely Presented Groups Based on the Notion of Discrete Curvature

  • I. G. Lysenok
Article

Abstract

A sufficient condition for the hyperbolicity of a group presented in terms of generators and defining relations is considered. The condition is formulated in terms of the negativity of a discrete analog of curvature for the Lyndon–van Kampen diagrams over a presentation of a group and is a generalization of the small cancellation condition.

Keywords

finitely presented group hyperbolic group 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia
  2. 2.Stevens Institute of TechnologyHobokenUSA

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