The Dehn function of a finitely presented group, first introduced by Gromov, is a useful invariant that is closely related to the solubility of the group’s word problem. It is well known that a finitely presented group is word hyperbolic if and only if it has sub-quadratic (and thus linear) Dehn function. A result of Ghys and de la Harpe states that no word hyperbolic group can have a (finitely generated) infinite torsion subgroup. We show that the same does not hold for finitely presented groups with Dehn function as small as cubic. In particular, for every m≥2 and sufficiently large odd integer n, there exists an embedding of the free Burnside group B(m,n) into a finitely presented group with cubic Dehn function.
This video is part of the New York Group Theory Cooperative‘s group theory seminar series.
