Mathematical Notes

, Volume 69, Issue 3–4, pp 575–577 | Cite as

One-Relator Groups of Exponential Growth Have Uniformly Exponential Growth

  • R. I. Grigorchuk
  • P. de la Harpe
growth of groups exponential growth uniformly exponential growth one-relator groups 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. Bucher and P. de la Harpe, “Free products with amalgamation and HNN-extensions which are of uniformly exponential growth,” Math. Notes (2001) (to appear).Google Scholar
  2. 2.
    M. Gromov, J. Lafontaine, and P. Pansu, Structures métriques pour les variétés riemanniennes, Cedic/F. Nathan, 1981.Google Scholar
  3. 3.
    R. I. Grigorchuk and P. de la Harpe, J. Dynamical Control Systems, 3 (1997), no. 1, 51–89.Google Scholar
  4. 4.
    P. de la Harpe and Topics in Geometric Group Theory, University of Chicago Press (to appear).Google Scholar
  5. 5.
    T. G. Ceccherini-Silberstein and R. I. Grigorchuk, Enseign. Math., 43 (1997), 337–354.Google Scholar
  6. 6.
    A. Karras and D. Solitar, Canad. J. Math., 23 (1971), 627–643.Google Scholar
  7. 7.
    B. Baumslag and S. J. Pride, J. London Math. Soc., 17 (1978), 435–436.Google Scholar
  8. 8.
    M. Gromov, Publ. Math. IHES, and 56 (1982), 5–100.Google Scholar
  9. 9.
    P. B. Shalen and P. Wagreich, Trans. Amer. Math. Soc., 331 (1992), 895–917.Google Scholar
  10. 10.
    G. Baumslag and P. B. Shalen, Comment. Math. Helvetici, 65 (1990), 243–254.Google Scholar
  11. 11.
    R. C. Lyndon and P. E. Schupp, Combinatorial Group Theory, vol. 89, Ergeb. Math. Grenzgeb, Springer, Berlin, 1977.Google Scholar
  12. 12.
    D. B. A. Epstein, Quart. J. Math. Oxford, and 12 (1961), 205–212.Google Scholar

Copyright information

© Plenum Publishing Corporation 2001

Authors and Affiliations

  • R. I. Grigorchuk
    • 1
  • P. de la Harpe
    • 2
  1. 1.V. A. Steklov Mathematics Institute, Russian Academy of SciencesRussia
  2. 2.Section de MathématiquesUniversité de GenèveRussia

Personalised recommendations