Geometry & Topology Volume 21, issue 4 (2017)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author index

To appear

Other MSP journals

Growth and order of automorphisms of free groups and free Burnside groups

Rémi Coulon and Arnaud Hilion

Geometry & Topology 21 (2017) 1969–2014

DOI: 10.2140/gt.2017.21.1969

Bibliography

1	S I Adian, The Burnside problem and identities in groups, 95, Springer (1979) MR537580
2	P Arnoux, V Berthé, A Hilion, A Siegel, Fractal representation of the attractive lamination of an automorphism of the free group, Ann. Inst. Fourier (Grenoble) 56 (2006) 2161 MR2290778
3	M Bestvina, M Feighn, M Handel, Laminations, trees, and irreducible automorphisms of free groups, Geom. Funct. Anal. 7 (1997) 215 MR1445386
4	M Bestvina, M Feighn, M Handel, The Tits alternative for Out(Fn), I : Dynamics of exponentially-growing automorphisms, Ann. of Math. 151 (2000) 517 MR1765705
5	M Bestvina, M Feighn, M Handel, The Tits alternative for Out(Fn), II : A Kolchin type theorem, Ann. of Math. 161 (2005) 1 MR2150382
6	M Bestvina, M Handel, Train tracks and automorphisms of free groups, Ann. of Math. 135 (1992) 1 MR1147956
7	W Burnside, On an unsettled question in the theory of discontinuous groups, Quart. J. 33 (1902) 230
8	E A Cherepanov, Free semigroup in the group of automorphisms of the free Burnside group, Comm. Algebra 33 (2005) 539 MR2124343
9	M Clay, A Pettet, Twisting out fully irreducible automorphisms, Geom. Funct. Anal. 20 (2010) 657 MR2720227
10	M M Cohen, M Lustig, Very small group actions on R–trees and Dehn twist automorphisms, Topology 34 (1995) 575 MR1341810
11	M Coornaert, T Delzant, A Papadopoulos, Géométrie et théorie des groupes, 1441, Springer (1990) MR1075994
12	R Coulon, A criterion for detecting trivial elements of Burnside groups, preprint (2012) arXiv:1211.4267
13	R Coulon, Outer automorphisms of free Burnside groups, Comment. Math. Helv. 88 (2013) 789 MR3134411
14	R Coulon, On the geometry of Burnside quotients of torsion free hyperbolic groups, Internat. J. Algebra Comput. 24 (2014) 251 MR3211906
15	R B Coulon, Partial periodic quotients of groups acting on a hyperbolic space, Ann. Inst. Fourier (Grenoble) 66 (2016) 1773 MR3533270
16	M Culler, J W Morgan, Group actions on R–trees, Proc. London Math. Soc. 55 (1987) 571 MR907233
17	T Delzant, M Gromov, Courbure mésoscopique et théorie de la toute petite simplification, J. Topol. 1 (2008) 804 MR2461856
18	D Gaboriau, A Jaeger, G Levitt, M Lustig, An index for counting fixed points of automorphisms of free groups, Duke Math. J. 93 (1998) 425 MR1626723
19	F Gautero, Combinatorial mapping-torus, branched surfaces and free group automorphisms, Ann. Sc. Norm. Super. Pisa Cl. Sci. 6 (2007) 405 MR2370267
20	F Gautero, M Lustig, The mapping-torus of a free group automorphism is hyperbolic relative to the canonical subgroups of polynomial growth, preprint (2007) arXiv:0707.0822
21	M Hall Jr., Solution of the Burnside problem for exponent six, Illinois J. Math. 2 (1958) 764 MR0102554
22	S V Ivanov, The free Burnside groups of sufficiently large exponents, Internat. J. Algebra Comput. 4 (1994) 1 MR1283947
23	J Karhumäki, On cube-free ω–words generated by binary morphisms, Discrete Appl. Math. 5 (1983) 279 MR690339
24	F Levi, B L van der Waerden, Über eine besondere Klasse von Gruppen, Abh. Math. Sem. Univ. Hamburg 9 (1933) 154 MR3069591
25	G Levitt, Counting growth types of automorphisms of free groups, Geom. Funct. Anal. 19 (2009) 1119 MR2570318
26	I G Lysënok, Infinite Burnside groups of even period, Izv. Ross. Akad. Nauk Ser. Mat. 60 (1996) 3 MR1405529
27	B Mossé, Puissances de mots et reconnaissabilité des points fixes d’une substitution, Theoret. Comput. Sci. 99 (1992) 327 MR1168468
28	J Nielsen, Die Isomorphismen der allgemeinen, unendlichen Gruppe mit zwei Erzeugenden, Math. Ann. 78 (1917) 385 MR1511907
29	P S Novikov, S I Adjan, Infinite periodic groups, I, Izv. Akad. Nauk SSSR Ser. Mat. 32 (1968) 212 MR0240179
30	P S Novikov, S I Adjan, Infinite periodic groups, II, Izv. Akad. Nauk SSSR Ser. Mat. 32 (1968) 251 MR0240179
31	P S Novikov, S I Adjan, Infinite periodic groups, III, Izv. Akad. Nauk SSSR Ser. Mat. 32 (1968) 709 MR0240179
32	A Y Ol’shanskiĭ, The Novikov–Adyan theorem, Mat. Sb. 118(160) (1982) 203, 287 MR658789
33	A Y Ol’shanskiĭ, Geometry of defining relations in groups, 70, Kluwer (1991) MR1191619
34	D Osin, Small cancellations over relatively hyperbolic groups and embedding theorems, Ann. of Math. (2) 172 (2010) 1
35	I N Sanov, Solution of Burnside’s problem for exponent 4, Leningrad State Univ. Annals Math. Ser. 10 (1940) 166 MR0003397
36	E Seneta, Non-negative matrices and Markov chains, Springer (2006) MR2209438
37	W P Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. 19 (1988) 417 MR956596