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Subgroup Distortion and the Relative Dehn Functions of Metabelian Groups

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 نشر من قبل Wenhao Wang
 تاريخ النشر 2021
  مجال البحث
والبحث باللغة English
 تأليف Wenhao Wang




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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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