On growth and torsion of groups

  • Laurent Bartholdi

    Georg-August-Universität Göttingen, Germany
  • Floriane Pochon

    Ecole Polytechnique Fédérale de Lausanne, Switzerland


We give a subexponential upper bound and a superpolynomial lower bound on the growth function of the Fabrykowski–Gupta group.

As a consequence, we answer negatively a question by Longobardi, Maj and Rhemtulla about characterizing groups containing no free subsemigroups on two generators.

Cite this article

Laurent Bartholdi, Floriane Pochon, On growth and torsion of groups. Groups Geom. Dyn. 3 (2009), no. 4, pp. 525–539

DOI 10.4171/GGD/68