Geodesic
An Approach to the Study of Finitely Presented Groups Based on the Notion of Discrete Curvature
Matematičeskie zametki, Tome 103 (2018) no. 4, pp. 568-575 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{MZM_2018_103_4_a7,
     author = {I. G. Lysenok},
     title = {An {Approach} to the {Study} of {Finitely} {Presented} {Groups} {Based} on the {Notion} of {Discrete} {Curvature}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {568--575},
     year = {2018},
     volume = {103},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_103_4_a7/}
}
TY  - JOUR
AU  - I. G. Lysenok
TI  - An Approach to the Study of Finitely Presented Groups Based on the Notion of Discrete Curvature
JO  - Matematičeskie zametki
PY  - 2018
SP  - 568
EP  - 575
VL  - 103
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/MZM_2018_103_4_a7/
LA  - ru
ID  - MZM_2018_103_4_a7
ER  - 
%0 Journal Article
%A I. G. Lysenok
%T An Approach to the Study of Finitely Presented Groups Based on the Notion of Discrete Curvature
%J Matematičeskie zametki
%D 2018
%P 568-575
%V 103
%N 4
%U http://geodesic.mathdoc.fr/item/MZM_2018_103_4_a7/
%G ru
%F MZM_2018_103_4_a7
I. G. Lysenok. An Approach to the Study of Finitely Presented Groups Based on the Notion of Discrete Curvature. Matematičeskie zametki, Tome 103 (2018) no. 4, pp. 568-575. http://geodesic.mathdoc.fr/item/MZM_2018_103_4_a7/

[1] D. B. A. Epstein, J. W. Cannon, D. F. Holt, S. V. F. Levy, M. S. Paterson, W. P. Thurston, Word Processing in Groups, Jones and Bartlett Publ., Boston, MA, 1992 | MR | Zbl

[2] R. Lindon, P. Shupp, Kombinatornaya teoriya grupp, Mir, M., 1980 | MR | Zbl

[3] M. Gromov, “Hyperbolic groups”, Essays in Group Theory, Math. Sci. Res. Inst. Publ., 8, Springer, New York, 1987, 75–263 | MR | Zbl

[4] D. L. Johnson, J. W. Wamsley, D. Wright, “The Fibonacci groups”, Proc. London Math. Soc. (3), 29 (1974), 577–592 | DOI | MR | Zbl

[5] Kourovskaya tetrad. Nereshennye voprosy teorii grupp, 18-e izd., dop., In-t matem. SO RAN, Novosibirsk, 2014