Verbal subgroups of hyperbolic groups have infinite width

Alexei Myasnikov; Andrey Nikolaev

doi:10.1112/jlms/jdu034

Verbal subgroups of hyperbolic groups have infinite width

Group Theory 2014-08-29 v5

Authors: Alexei Myasnikov , Andrey Nikolaev

View on arXiv ↗ PDF ↗ DOI ↗

Abstract

Let $G$ be a non-elementary hyperbolic group. Let $w$ be a group word such that the set $w[G]$ of all its values in $G$ does not coincide with $G$ or 1. We show that the width of verbal subgroup $w(G)=<w[G]>$ is infinite. That is, there is no such $l\in\mathbb Z$ that any $g\in w(G)$ can be represented as a product of $\le l$ values of $w$ and their inverses.

Keywords

hyperbolic groups finite group theory group theory

Cite

@article{arxiv.1107.3719,
  title  = {Verbal subgroups of hyperbolic groups have infinite width},
  author = {Alexei Myasnikov and Andrey Nikolaev},
  journal= {arXiv preprint arXiv:1107.3719},
  year   = {2014}
}

Comments

To appear in Journal of the London Mathematical Society. 22 pages, 8 figures

Verbal subgroups of hyperbolic groups have infinite width

Abstract

Keywords

Cite

Comments

Related papers