Abstract

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

Keywords

subgroup distortion, Thompson's group

Mathematical Subject Classification

Primary: 20F65

Authors