Verbal subgroups of hyperbolic groups have infinite width

Details Verbal subgroups of hyperbolic groups have infinite width Verbal subgroups of hyperbolic groups have infinite width

2011-07-19

arxiv.org/abs/1107.3719v2

Mathematics

Group Theory

16 pages, 6 figures

Scientific paper

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 $w(G)=$ 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.

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