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 language | English |
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Pages (from-to) | 573-591 |
Number of pages | 19 |
Journal | Journal of the London Mathematical Society |
Volume | 90 |
Issue number | 2 |
DOIs | |
State | Published - 1 Oct 2014 |