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. 525–539DOI 10.4171/GGD/68