Distortion of embeddings of a torsion-free finitely generated nilpotent group into a unitriangular group

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Abstract

In this paper, we study distortion of various well-known embeddings of finitely generated torsion-free nilpotent groups G into unitriangular groups UTn(ℤ). In particular, we show that there is no undistorted embeddings of 5-dimensional Heisenberg group into UTn(ℤ). We also provide a polynomial time algorithm for finding distortion of a given subgroup of G.

Original languageEnglish
Pages (from-to)633-653
Number of pages21
JournalInternational Journal of Algebra and Computation
Volume27
Issue number6
DOIs
StatePublished - 1 Sep 2017

Keywords

  • Heisenberg group
  • Jennings' embedding
  • Mal'cev basis
  • Nickel's embedding
  • Nilpotent groups
  • subgroup distortion
  • unitriangular groups

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