Groups, Geometry, and Dynamics

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Volume 3, Issue 4, 2009, pp. 525–539
DOI: 10.4171/GGD/68

Published online: 2009-12-23

On growth and torsion of groups

Laurent Bartholdi[1] and Floriane Pochon[2]

(1) Georg-August-Universität Göttingen, Germany
(2) 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.

Keywords: Word growth, free subsemigroup

Bartholdi Laurent, Pochon Floriane: On growth and torsion of groups. Groups Geom. Dyn. 3 (2009), 525-539. doi: 10.4171/GGD/68