José Burillo

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The goal of this paper is to construct quasi-isometrically embedded subgroups of Thompson’s group F which are isomorphic to F × Zn for all n. A result estimating the norm of an element of Thompson’s group is found. As a corollary, Thompson’s group is seen to be an example of a finitely presented group which has an infinite-dimensional asymptotic cone. The(More)
Here we describe the results of some computational explorations in Thompson’s group F . We describe experiments to estimate the cogrowth of F with respect to its standard finite generating set, designed to address the subtle and difficult question whether or not Thompson’s group is amenable. We also describe experiments to estimate the exponential growth(More)
This note records some observations concerning geodesic growth functions. If a nilpotent group is not virtually cyclic then it has exponential geodesic growth with respect to all finite generating sets. On the other hand, if a finitely generated group G has an element whose normal closure is abelian and of finite index, then G has a finite generating set(More)
Here we describe the results of some computational explorations in Thompson’s group F . We describe experiments to estimate the cogrowth of F with respect to its standard finite generating set, designed to address the subtle and difficult question whether or not Thompson’s group is amenable. We also describe experiments to estimate the exponential growth(More)
Thompson’s groups have been extensively studied since their introduction by Thompson in the 1960s, despite the fact that Thompson’s account [7] appeared only in 1980. They have provided examples of infinite finitely presented simple groups, as well as some other interesting counterexamples in group theory (see for example, Brown and Geoghegan [3]). Cannon,(More)