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Distortion of wreath products in some finitely presented groups

Sean Cleary
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Abstract

Wreath products such as Z wr Z are not finitely-presentable yet can occur as subgroups of finitely presented groups. Here we compute the distortion of Z wr Z as a subgroup of Thompson's group F and as a subgroup of Baumslag's metabelian group G. We find that Z wr Z is undistorted in F but is at least exponentially distorted in G.

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Sean Cleary. 2005-05-13. Distortion of wreath products in some finitely presented groups. https://arxiv.org/abs/math/0505288

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