Length and Area Functions on Groups and Quasi-Isometric Higman Embeddings

International Journal of Algebra and Computation

Volumn 11, Issue 2, 2001, Pages 137-170

  Oĺshanskii, Alexander Y U ^a,b   Sapir, Mark V ^a  

^a VANDERBILT UNIVERSITY   (United States)

^b MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035609044     PISSN: 02181967     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218196701000401     Document Type: Article

References (39)

1. S. I. Adian, The Burnside Problem and Identities in Groups, Springer-Verlag, 1979.
2. J. Alonso, Inégalités isopérimétriques et quasi-isométries, C. R. Acad. Sci. Paris Série 311 (1) (1990), 761-764.
3. G. Baumslag, M. R. Bridson, C. F. Miller III and H. Short, Finitely presented subgroups of automatic groups and their isoperimetric functions, J. London Math. Soc. 56 (2) (1997), 292-304.
4. G. Baumslag and J. E. Roseblade, Subgroups of direct products of free group, J. London Math. Soc. 30 (2) (1984), 44-52.
5. J. C. Birget, The complexity of the word problem for semigroups and the Higman embedding theorem, Int. J. Algebra Comput. 8 (1998), 235-294.
6. J. C. Birget, A. Yu. Olshanskii, E. Rips and M. Sapir, Isoperimetric functions of groups and computational complexity of the word problem, preprint (1998).
7. M. Bridson, Fractional isoperimetric inequalities and subgroup distortion (to appear).
8. M. G. Brin and C. C. Squier, Groups of piecewise linear homeomorphisms of the real line, Invent. Math. 79 (1985), 485-498.
9. D. J. Collins, Conjugacy and the Higman embedding theorem, in Word Problems II Conf., Decision Problems, Algebra, Oxford, 1976, pp. 81-85; Studies in Logic and the Foundations of Mathematics 95, North-Holland, Amsterdam, New York, 1980.
10. D. J. Collins, Conjugacy and the Higman embedding theorem, in Word Problems II Conf., Decision Problems, Algebra, Oxford, 1976, pp. 81-85; Studies in Logic and the Foundations of Mathematics 95, North-Holland, Amsterdam, New York, 1980.
11. D. B. A. Epstein, et al., Word processing in groups, Jones and Bartlett, Boston, MA, 1992.
12. B. Farb, The extrinsic geometry of subgroups and the generalized word problem, Proc. London Math. Soc. 68 (3) (1994), 577-593.
13. 1 -norms for finite presentations, in Algorithms and Classification in Combinatorial Group Theory, eds. G. Baumslag and C. F. Miller, MSRI Publications 23, Springer-Verlag, 1992.
14. S. M. Gersten, Preservation and distortion of area in finitely presented groups, GAFA 6 (1996), 301-345.
15. S. M. Gersten, Isodiametric and isoperimetric functions of finite presentations, in Geometric Group Theory, Vol. 1, eds. G. A. Niblo and A. Roller, London Math. Soc., Lecture Notes Series 181, Cambridge University Press, 1993, pp. 79-96.
16. M. Gromov, Hyperbolic manifolds (according to Thurston and Jorgensen), Bourbaki Seminar, Vol. 1979/80, Lecture Notes in Mathematics, 842, Springer, Berlin, New York, 1981, pp. 40-53.
17. M. Gromov, Asymptotic invariants of infinite groups, in Geometric Group Theory, Vol. 2, eds. G. A. Niblo and M. A. Roller, London Math. Soc., Lecture Notes Series 182, 1993.
18. V. Guba and M. Sapir, Diagram groups, Memoirs AMS, 130 (620) (November 1997).
19. V. Guba and M. Sapir, The Dehn function of a free product of non-trivial groups is superadditive, Proc. Amer. Math. Soc. (1999).
20. Kourovka, Notebook: Unsolved Problems in Group Theory, 5th edition, Novosibirsk, 1976.
21. O. Kharlampovich and M. Sapir, Algorithmic problems in varieties, 5 (4)-(5) (1995), 379-602.
22. E. M. Levich, The representation of two-step-solvable groups by matrices over a field of characteristic zero, Mat. Sb. 81 (1970), 352-357.
23. R. Lyndon and P. Schupp, Combinatorial Group Theory, Springer-Verlag, 1977.
24. Yu. I. Manin, Vychislimoe i nevychislimoe, Computable and non-computable, Moscow, Soviet Radio, 1980.
25. K. Madlener and F. Otto, Pseudo-natural algorithms for the word problem for finitely presented monoids and groups, J. Symbo. Comput. 1 (1985), 383-418.
26. C. F. Miller III, On group-theoretic decision problems and their classification, Ann. Math. Stud. 68 (1971), Princeton University Press, Princeton, New Jersey.
27. A. Yu. Ol'shanskii, The Geometry of Defining Relations in Groups, Kluwer Academic Publishers, 1991.
28. A. Yu. Ol'shanskii, The SQ-universality of hyperbolic groups, Mat. Sb. 186 (8) (1995), 119-132.
29. A. Yu. Ol'shanskii, Distortion functions for subgroups, in Geometric Group Theory Down Under, Proc. of a Special Year in Geometric Group Theory, Canberra, Australia, 1996, eds. J. Cossey, ..., Walter de Gruyter, Berlin, New York, 1997, pp. 281-291.
30. A. Yu. Ol'shanskii, On distortion of subgroups in finitely presented groups, Mat. Sb. 188 (11) (1997), 51-98.
31. A. Yu. Ol'shanskii and M. V. Sapir, Embeddings of relatively free groups into finitely presented groups (accepted in Contemp. Math.).
32. A. Yu. Ol'shanskii and M. V. Sapir, Length functions on subgroups of finitely presented groups, in Groups-Kozea 98, Proc. Intern. Conf. Pusan, Korea, 1998, eds. Young Gheel Baik, ..., Walter de Gruyter, Berlin, New York, 2000, pp. 297-304.
33. A. Yu. Ol'shanskii and M. V. Sapir, A Higman embedding preserving the solvablity of the conjugacy problem, in preparation (2000).
34. P. Papasoglu On the asymptotic cone of groups satisfying a quadratic isoperimetric inequality, J. Diff. Geom. 44 (4) (1996), 789-806.
35. V. N. Remeslennikov, Representation of finitely generated metabelian groups by matrices, Algebra i Logika, 8 (1969), 72-75.
36. J. Rotman, An Introduction to the Theory of Groups, 3rd edition, Allyn and Bacon, 1984.
37. M. V. Sapir, J. C. Birget and E. Rips, Isoperimetric and isodiametric functions of groups, submitted.
38. D. Segal, Polycyclic groups, Cambridge University Press, Cambridge, 1983.
39. B. A. F. Wehrfritz, On finitely generated soluble linear groups, Math. Z. 170 (2) (1980), 155-167.