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arXiv · 2104.11828

Subgroup Distortion and the Relative Dehn Functions of Metabelian Groups

Wenhao Wang
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Abstract

We show the connection between the relative Dehn function of a finitely generated metabelian group and the distortion function of a corresponding subgroup in the wreath product of two free abelian groups of finite rank. Further, we show that if a finitely generated metabelian group $G$ is an extension of an abelian group by $\mathbb Z$ the relative Dehn function of $G$ is polynomially bounded. Therefore, if $G$ is finitely presented, the Dehn function is bounded above by the exponential function up to equivalence.

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Wenhao Wang. 2021-04-23. Subgroup Distortion and the Relative Dehn Functions of Metabelian Groups. https://arxiv.org/abs/2104.11828

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