JournalsggdVol. 3 , No. 4DOI 10.4171/ggd/68

On growth and torsion of groups

  • Laurent Bartholdi

    Georg-August-Universität Göttingen, Germany
  • Floriane Pochon

    Ecole Polytechnique Fédérale de Lausanne, Switzerland
On growth and torsion of groups cover


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.