Home / Publications / Published articles / Metric Properties and Distortion in Nilpotent Groups

José Burillo and Eric L Platón (2014)

Metric Properties and Distortion in Nilpotent Groups

In: Extended Abstracts Fall 2012, ed. by González-Meneses, Juan and Lustig, Martin and Ventura, Enric, pp. 25–27, Springer International Publishing. Trends in Mathematics. (ISBN: 978-3-319-05487-2, 978-3-319-05488-9).

IntroductionOne of the concepts developed to study groups from the metric point of view is the concept of distortion of a subgroup in a group. The concept appears already in Gromov’s paper [2], and has been studied by several authors, such as Bridson [1], or Sapir and Ol’shanskii (see [3] and [4]). In this paper we study distortion functions obtained by several nilpotent groups embedded into each other. The two families studied are Heisenberg groups and the groups of unipotent upper-triangular matrices. As it could be expected, distortion is polynomial in all cases, and precise degrees are computed for different embeddings between them. The main tool to study this distortion are the estimates of the metric, quantities that can be easily computed for a given element (and its normal form) and which differ from the actual metric by a multiplicative constant. Hence, these estimates are sufficient to compute the distortion functions, and allow us to obtain precise values for them. Some resu

Group Theory and Generalizations

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