Geodesic
Complementing a finite subgroup of a hyperbolic group by a free factor
Algebra i logika, Tome 49 (2010) no. 4, pp. 520-554 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We give necessary and sufficient conditions for a finite subgroup $H$ of a hyperbolic group $G$ to contain a free subgroup $F$ of rank two in $G$ such that $F$ and $H$ generate a free product $F*H$. A verification algorithm for these conditions is pointed out.
Keywords: hyperbolic group, finite subgroup, free product. 
@article{AL_2010_49_4_a4,
     author = {K. S. Sviridov},
     title = {Complementing a~finite subgroup of a~hyperbolic group by a~free factor},
     journal = {Algebra i logika},
     pages = {520--554},
     year = {2010},
     volume = {49},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2010_49_4_a4/}
}
TY  - JOUR
AU  - K. S. Sviridov
TI  - Complementing a finite subgroup of a hyperbolic group by a free factor
JO  - Algebra i logika
PY  - 2010
SP  - 520
EP  - 554
VL  - 49
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/AL_2010_49_4_a4/
LA  - ru
ID  - AL_2010_49_4_a4
ER  - 
%0 Journal Article
%A K. S. Sviridov
%T Complementing a finite subgroup of a hyperbolic group by a free factor
%J Algebra i logika
%D 2010
%P 520-554
%V 49
%N 4
%U http://geodesic.mathdoc.fr/item/AL_2010_49_4_a4/
%G ru
%F AL_2010_49_4_a4
K. S. Sviridov. Complementing a finite subgroup of a hyperbolic group by a free factor. Algebra i logika, Tome 49 (2010) no. 4, pp. 520-554. http://geodesic.mathdoc.fr/item/AL_2010_49_4_a4/

[1] É. Ghys, P. de la Harpe (eds.), Sur les groupes hyperboliques d'faprés Mikhael Gromov, Progress Math., 83, Birkhäuser, Boston, MA, 1990 ; E. Gis, P. de lya Arp (red.), Giperbolicheskie gruppy po Mikhailu Gromovu, Mir, M., 1992 | MR | Zbl | MR

[2] O. V. Bogopolskii, V. N. Gerasimov, “Konechnye podgruppy giperbolicheskikh grupp”, Algebra i logika, 34:6 (1995), 619–622 | MR

[3] N. Brady, “Finite subgroups of hyperbolic groups”, Int. J. Algebra Comput., 10:4 (2000), 399–405 | DOI | MR | Zbl

[4] M. R. Bridson, A. Haefliger, Metric spaces of non-positive curvature, Grundlehren Mathem. Wiss., 319, Springer-Verlag, Berlin, 1999 | MR | Zbl

[5] R. C. Lyndon, P. E. Schupp, Combinatorial group theory, Ergebn. Math. Grenzg., 89, Springer-Verlag, Berlin–Heidelberg–New York, 1977 ; R. Lindon, P. Shupp, Kombinatornaya teoriya grupp, Mir, M., 1980 | MR | Zbl | MR

[6] S. Billington, D. Epstein, D. Holt, Geodesics in word hyperbolic groups http://www.maths.warwick.ac.uk/~dbae/papers/geod.ps