References
M.Benson, On the rational growth of virtually nilpotent groups. In: Combinatorial Group Theory, S. M. Gersten and J. R. Stallings (eds.). Ann. of Math. Stud.111 (1987).
N.Billington, The growth of stratified groups. Ph.D. thesis, La Trobe University 1986.
J. W.Cannon, The growth of the closed surface groups and compact hyperbolic groups. Preprint.
J. W. Cannon, The combinatorial structure of co-compact discrete hyperbolic groups. Geom. Dedicata16, 123–148 (1984).
D. J.Collins, M.Edjvet and C. P.Gill, Growth series for the group 〈x,y¦x −1 yx=y l〉. Preprint.
M. Edjvet andD. L. Johnson, The growth of certain amalgamated free products and HNN-extensions. J. Austral. Math. Soc. Ser. A52, 285–298 (1992).
W. J. Floyd andS. P. Plotnick, Growth functions on Fuchsian groups and the Euler characteristic. Invent. Math.88, 1–29 (1987).
W. J. Floyd andS. P. Plotnick, Symmetries of planar growth functions. Invent. Math.93, 501–543 (1988).
M. A.Grayson, Geometry and growth in three dimensions. Ph.D. thesis, Princeton University (1983).
D. L. Johnson, Rational growth of wreath products. In: Groups St. Andrews 1989. London Math. Soc. Lecture Note Ser.160, 309–315 (1991).
D. L.Johnson and H. J.Song, The growth of the Gieseking group. Preprint.
J. Lewin, The growth function of some free products of groups. Comm. Algebra17, 1187–1191 (1989).
R. C.Lyndon and P. E.Schupp, Combinatorial Group Theory. Berlin-Heidelberg-New York 1977.
J. Milnor, A note on curvature and fundamental groups. J. Differential Geom.2, 1–7 (1968).
W. Parry, Counterexamples involving growth series and the Euler characteristic. Proc. Amer. Math. Soc.102, 49–51 (1988).
M. Shapiro, A geometric approach to the almost convexity and growth of some nilpotent groups. Math. Ann.285, 601–624 (1989).
N. J. Smythe, Growth functions and Euler series. Invent. Math.77, 517–531 (1984).
Author information
Authors and Affiliations
Additional information
Supported by SERC Postgraduate Award.
Rights and permissions
About this article
Cite this article
Collins, D.J., Edjvet, M. & Gill, C.P. Growth series for the group 〈x,y¦x −1 yx=y l〉. Arch. Math 62, 1–11 (1994). https://doi.org/10.1007/BF01200431
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01200431