2021/04/23 by Wenhao Wang, Wang, Wenhao
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #math.GR
paper · pdf · doi:10.48550/arxiv.2104.11828
16 pages, 2 figures. Comments are welcome!
arxiv created 2021/04/23 · arxiv updated 2021/04/27
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.