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Exponentially distorted subgroups in wreath products
The subgroup $H = \langle \, x, \, y, \, [x,a]a, \, [y,a]a \, \rangle$ is exponentially distorted in $\mathbb{Z} \wr F_2$ where $\mathbb{Z} = \langle{a}\rangle$ and $F_2 = F(x,y)$. The same is true in $\mathbb{Z} \wr ( \mathbb{Z} \wr \mathbb{Z}) = \langle a \rangle \wr ( \langle s \rangle \wr \langle t \rangle)$ with $x=ts$ and $y=t$. |