Geodesic
Growth of periodic quotients of hyperbolic groups
Coulon, Rémi1
1Department of Mathematics, Vanderbilt University, Stevenson Center 1326, Nashville, TN 37240, USA
Algebraic and Geometric Topology, Tome 13 (2013) no. 6, pp. 3111-3133
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

Let G be a non-elementary torsion-free hyperbolic group. We prove that the exponential growth rate of the periodic quotient G∕Gn tends to the one of G as n odd approaches infinity. Moreover, we provide an estimate for the rate at which the convergence is taking place.

DOI : 10.2140/agt.2013.13.3111
Keywords: periodic groups, exponential growth, hyperbolic groups

Coulon, Rémi  1

1 Department of Mathematics, Vanderbilt University, Stevenson Center 1326, Nashville, TN 37240, USA 
@article{10_2140_agt_2013_13_3111,
     author = {Coulon, R\'emi},
     title = {Growth of periodic quotients of hyperbolic groups},
     journal = {Algebraic and Geometric Topology},
     pages = {3111--3133},
     year = {2013},
     volume = {13},
     number = {6},
     doi = {10.2140/agt.2013.13.3111},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2013.13.3111/}
}
TY  - JOUR
AU  - Coulon, Rémi
TI  - Growth of periodic quotients of hyperbolic groups
JO  - Algebraic and Geometric Topology
PY  - 2013
SP  - 3111
EP  - 3133
VL  - 13
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2013.13.3111/
DO  - 10.2140/agt.2013.13.3111
ID  - 10_2140_agt_2013_13_3111
ER  - 
%0 Journal Article
%A Coulon, Rémi
%T Growth of periodic quotients of hyperbolic groups
%J Algebraic and Geometric Topology
%D 2013
%P 3111-3133
%V 13
%N 6
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2013.13.3111/
%R 10.2140/agt.2013.13.3111
%F 10_2140_agt_2013_13_3111
Coulon, Rémi. Growth of periodic quotients of hyperbolic groups. Algebraic and Geometric Topology, Tome 13 (2013) no. 6, pp. 3111-3133. doi: 10.2140/agt.2013.13.3111

[1] S I Adian, The Burnside problem and identities in groups, Ergeb. Math. Grenzgeb. 95, Springer (1979)

[2] G N Arzhantseva, I G Lysenok, Growth tightness for word hyperbolic groups, Math. Z. 241 (2002) 597

[3] V S Atabekyan, Uniform nonamenability of subgroups of free Burnside groups of odd period, Mat. Zametki 85 (2009) 516

[4] W Burnside, On an unsettled question in the theory of discontinuous groups, Quart. J. Pure Appl. Math. 33 (1902) 230

[5] J W Cannon, The combinatorial structure of cocompact discrete hyperbolic groups, Geom. Dedicata 16 (1984) 123

[6] M Coornaert, Mesures de Patterson–Sullivan sur le bord d'un espace hyperbolique au sens de Gromov, Pacific J. Math. 159 (1993) 241

[7] M Coornaert, T Delzant, A Papadopoulos, Géométrie et théorie des groupes, Lecture Notes in Mathematics 1441, Springer (1990)

[8] R Coulon, Detecting trivial elements of Burnside groups

[9] T Delzant, Sous-groupes distingués et quotients des groupes hyperboliques, Duke Math. J. 83 (1996) 661

[10] T Delzant, M Gromov, Courbure mésoscopique et théorie de la toute petite simplification, J. Topol. 1 (2008) 804

[11] É Ghys, P De La Harpe, Editors, Sur les groupes hyperboliques d'après Mikhael Gromov, Progress in Mathematics 83, Birkhäuser (1990)

[12] M Gromov, Hyperbolic groups, from: "Essays in group theory", Math. Sci. Res. Inst. Publ. 8, Springer (1987) 75

[13] M Hall Jr., Solution of the Burnside problem of exponent 6, Proc. Nat. Acad. Sci. U.S.A. 43 (1957) 751

[14] S V Ivanov, The free Burnside groups of sufficiently large exponents, Internat. J. Algebra Comput. 4 (1994)

[15] M Koubi, Croissance uniforme dans les groupes hyperboliques, Ann. Inst. Fourier (Grenoble) 48 (1998) 1441

[16] F Levi, B L Van Der Waerden, Über eine besondere Klasse von Gruppen, Abh. Math. Sem. Univ. Hamburg 9 (1933) 154

[17] I G Lysënok, Infinite Burnside groups of even period, Izv. Ross. Akad. Nauk Ser. Mat. 60 (1996) 3

[18] S P Novikov, Adams operators and fixed points, Izv. Akad. Nauk SSSR Ser. Mat. 32 (1968) 1245

[19] A Y Ol’Shanskiĭ, The Novikov–Adyan theorem, Mat. Sb. 118(160) (1982) 203, 287

[20] A Y Ol’Shanskiĭ, Periodic quotient groups of hyperbolic groups, Mat. Sb. 182 (1991) 543

[21] D V Osin, Uniform non-amenability of free Burnside groups, Arch. Math. $($Basel$)$ 88 (2007) 403

[22] I N Sanov, Solution of Burnside's problem for exponent 4, Leningrad State Univ. Annals [Uchenye Zapiski] Math. Ser. 10 (1940) 166

Cité par Sources :