Verbal subgroups of hyperbolic groups have infinite width

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Abstract

Let G be a non-elementary hyperbolic group. Let w be a proper group word. We show that the width of the verbal subgroup w(G) = <w[G]> is infinite. That is, there is no l ε Z such that any g ε w(G) can be represented as a product of at most l values of w and their inverses. As a consequence, we obtain the same result for a wide class of relatively hyperbolic groups.

Original languageEnglish
Pages (from-to)573-591
Number of pages19
JournalJournal of the London Mathematical Society
Volume90
Issue number2
DOIs
StatePublished - 1 Oct 2014

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