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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  ∈  Z    such that any    g  ∈  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.

Verbal subgroups of hyperbolic groups have infinite width