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

Funda Gul; Alexei G. Myasnikov; Mahmood Sohrabi

doi:10.1142/S021819671750031X

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

Stevens Institute of Technology

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	633-653
Number of pages	21
Journal	International Journal of Algebra and Computation
Volume	27
Issue number	6
DOIs	https://doi.org/10.1142/S021819671750031X
State	Published - 1 Sep 2017

Keywords

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

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10.1142/S021819671750031X

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title = "Distortion of embeddings of a torsion-free finitely generated nilpotent group into a unitriangular group",

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.",

keywords = "Heisenberg group, Jennings' embedding, Mal'cev basis, Nickel's embedding, Nilpotent groups, subgroup distortion, unitriangular groups",

author = "Funda Gul and Myasnikov, \{Alexei G.\} and Mahmood Sohrabi",

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AU - Gul, Funda

AU - Myasnikov, Alexei G.

AU - Sohrabi, Mahmood

PY - 2017/9/1

Y1 - 2017/9/1

N2 - 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.

AB - 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.

KW - Heisenberg group

KW - Jennings' embedding

KW - Mal'cev basis

KW - Nickel's embedding

KW - Nilpotent groups

KW - subgroup distortion

KW - unitriangular groups

UR - https://www.scopus.com/pages/publications/85028807183

UR - https://www.scopus.com/pages/publications/85028807183#tab=citedBy

U2 - 10.1142/S021819671750031X

DO - 10.1142/S021819671750031X

M3 - Article

AN - SCOPUS:85028807183

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VL - 27

SP - 633

EP - 653

JO - International Journal of Algebra and Computation

JF - International Journal of Algebra and Computation

IS - 6

ER -

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

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Keywords

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