Bounded rank subgroups of coxeter groups, Artin groups and one-relator groups with torsion

Proceedings of the London Mathematical Society

Volumn 88, Issue 1, 2004, Pages 89-113

  Kapovich, Ilya ^a   Schupp, Paul ^a  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 1442304192     PISSN: 00246115     EISSN: None     Source Type: Journal    
DOI: 10.1112/S0024611503014345     Document Type: Conference Paper

References (48)

1. I. AGOL, D. LONG and A. REID, 'The Blanchi groups are separable on geometrically finite subgroups', Ann. of Math. (2) 153 (2001) 599-621.
2. J. ALONSO, T. BRADY, D. COOPER, V. FERLINI, M. LUSTIG, M. MIHALIK, M. SHAPIRO and H. SHORT, 'Notes on hyperbolic groups', Group theory from a geometrical viewpoint (ed. É. Ghys, A. Haefliger and A. Verjovsky), Trieste, 1990 (World Scientific, River Edge, NJ, 1991) 3-63.
3. K. APPEL and P. SCHUPP, 'Artin groups and infinite Coxeter groups', Invent. Math. 72 (1983) 201-220.
4. G. ARZHANTSEVA, 'On groups in which subgroups with a fixed number of generators are free', Fundam. Prikl. Mat. 3 (1997) 675-683 (Russian).
5. G. ARZHANTSEVA, 'Generic properties of finitely presented groups and Howson's theorem', Comm. Algebra 26 (1998) 3783-3792.
6. G. ARZHANTSEVA, 'A property of subgroups of infinite index in a free group', Proc. Amer. Math. Soc. 128 (2000) 3205-3210.
7. G. ARZHANTSEVA and A. OL'SHANSKII, 'Genericity of the class of groups in which subgroups with a lesser number of generators are free', Mat. Zametki 59 (1996) 489-496 (Russian).
8. J. BECKER, M. HORAK and L. VANWYK, 'Presentations of subgroups of Artin groups', Missouri J. Math. Sci. 10 (1998) 3-14.
9. M. BESTVINA, 'Non-positively curved aspects of Artin groups of finite type', Geom. Topol. 3 (1999) 269-302.
10. M. BESTVINA and N. BRADY, 'Morse theory and finiteness properties of groups', Invent. Math. 129 (1997) 445-470.
11. N. BOURBAKI, Éléments de mathématique, Fasc. XXXIV, Groupes et algèbres de Lie: Chapitre IV, Groupes de Coxeter et systèmes de Tits; Chapitre V, Groupes engendrés par des réflexions; Chapitre VI, Systèmes de racines, Actualités Scientifiques et Industrielles 1337 (Hermann, Paris, 1968).
12. I. BUMAGIN, 'On small cancellation k-generated groups with (k-1)-generated subgroups all free'. Internat. J. Algebra Comput. 11 (2001) 507-524.
13. K.-U. BUX and C. GONZALEZ, 'The Bestvina-Brady construction revisited: geometric computation of Σ-invariants for right-angled Artin groups', J. London Math. Soc. (2) 60 (1999) 793-801.
14. R. CHARNEY and M. DAVIS, 'When is a Coxeter system determined by its Coxeter group?', J. London Math. Soc. (2) 61 (2000) 441-461.
15. M. COORNAERT, T. DELZANT and A. PAPADOPOULOS, Géométrie et théorie des groupes. Les groupes hyperboliques de Gromov, Lecture Notes in Mathematics 1441 (Springer, Berlin, 1990).
16. J. CRISP, 'Symmetrical subgroups of Artin groups', Adv. Math. 152 (2000) 159-177.
17. J. CRISP and L. PARIS, 'The solution to a conjecture of Tits on the subgroup generated by the squares of the generators of an Artin group', Invent. Math. 145 (2001) 19-36.
18. M. DAVIS and T. JANUSZKIEWICZ, 'Right-angled Artin groups are commensurable with right-angled Coxeter groups', J. Pure Appl. Algebra 153 (2000) 229-235.
19. W. DICKS and I. LEARY, 'Presentations for subgroups of Artin groups', Proc. Amer. Math. Soc. 127 (1999) 343-348.
20. S. GERSTEN and H. SHORT, 'Rational subgroups of biautomatic groups', Ann. of Math. (2) 134 (1991) 125-158.
21. É. GHYS and P. DE LA HARPE (eds), Sur les groupes hyperboliques d'aprés Mikhael Gromov, Progress in Mathematics 83 (Birkhäuser, Boston, 1990).
22. R. GITIK, 'Doubles of groups and hyperbolic LERF 3-manifolds', Ann. of Math. (2) 150 (1999) 775-806.
23. R. GITIK, 'On the profinite topology on Coxeter groups', Preprint, Institut des Hautes Études Scientifiques, 2001.
24. G. A. GUREVICH, 'On the conjugacy problem for one-relator groups', Dokl. Akad. Nauk SSSR Ser. Mat. 207 (1972) 1436-1439.
25. T. HSU and D. WISE, 'Separating quasiconvex subgroups of right-angled Artin groups', Math. Z. 240 (2002) 521-548.
26. I. KAPOVICH and A. MYASNIKOV, 'Stallings foldings and the subgroup structure of free groups', J. Algebra 248 (2002) 608-668.
27. I. KAPOVICH and H. SHORT, 'Greenberg's theorem for quasiconvex subgroups of word hyperbolic groups', Canad. J. Math. 48 (1996) 1224-1244.
28. A. KARRASS, W. MAGNUS and D. SOLITAR, 'Elements of finite order in groups with a single defining relation', Comm. Pure Appl. Math. 13 (1960) 57-66.
29. H. VAN DER LEK, 'The homotopy type of complex hyperplane complements', PhD Thesis, University of Nijmegen, Nijmegen, 1983.
30. D. LONG and G. NIBLO, 'Subgroup separability and 3-manifold groups', Math. Z. 207 (1991) 209-215.
31. D. LONG and A. REID, 'The fundamental group of the double of the figure-eight knot exterior is GFERF', Bull London Math. Soc. 33 (2001) 391-396.
32. D. LONG and A. REID, 'On subgroup separability in hyperbolic Coxeter groups', Geom. Dedicate 87 (2001) 245-260.
33. R. LYNDON and P. SCHUPP, Combinatorial group theory (Springer, Berlin, 1977, reprinted in the Classics in Mathematics series, Springer, Berlin, 2000).
34. P in a free group', Michigan Math. J. 9 (1962) 289-298.
35. J. McCAMMOND and D. WISE, 'Coherence, local quasiconvexity and the perimeter of 2-complexes', Preprint, Cornell University, 1998.
36. J. MEIER, H. MEINERT and L. VANWYK, 'On the Σ-invariants of Artin groups', Topology Appl. 110 (2001) 71-81.
37. M. MIHALIK and W. TOWLE, 'Quasiconvex subgroups of negatively curved groups', J. Pure Appl. Algebra 95 (1994) 297-301.
38. B. B. NEWMAN, 'Some results on one-relator groups', Bull. Amer. Math. Soc. 74 (1968) 568-571.
39. G. NIBLO and D. WISE, 'Subgroup separability, knot groups and graph manifolds', Proc. Amer. Math. Soc. 129 (2001) 685-693.
40. L. PARIS, 'Parabolic subgroups of Artin groups', J. Algebra 196 (1997) 369-399.
41. S. PRIDE, 'The two-generator subgroups of one-relator groups with torsion', Trans. Amer. Math. Soc. 234 (1977) 483-496.
42. P. SCHUPP, 'A strengthened Freiheitssatz', Math. Ann. 221 (1976) 73-80.
43. P. SCHUPP, 'Coxeter groups, 2-completion, perimeter reduction and subgroup separability', Geom. Dedicate 96 (2003) 179-198.
44. P. SCOTT, 'Subgroups of surface groups are almost geometric', J. London Math. Soc. (2) 17 (1978) 555-565.
45. H. SHORT, 'Quasiconvexity and a theorem of Howson's', Group theory from a geometrical viewpoint (ed. É. Ghys, A. Haefliger and A. Verjovsky), Trieste, 1990 (World Scientific, River Edge, NJ, 1991) 168-176.
46. J. R. STALLINGS, 'Topology of finite graphs', Invent. Math. 71 (1983) 551-565.
47. G. A. SWARUP, 'Geometric finiteness and rationality', J. Pure Appl. Algebra 86 (1993) 327-333.
48. D. WISE, 'Subgroup separability of the figure 8 knot group', Preprint, McGill University, 2000.