Palindromic Width of Wreath Products
Abstract
We show that the wreath product $G \wr \mathbb{Z}^n$ of any finitely generated group $G$ with $\mathbb{Z}^n$ has finite palindromic width. We also show that $C \wr A$ has finite palindromic width if $C$ has finite commutator width and $A$ is a finitely generated infinite abelian group. Further we prove that if $H$ is a nonabelian group with finite palindromic width and $G$ any finitely generated group, then every element of the subgroup $G' \wr H$ can be expressed as a product of uniformly boundedly many palindromes. From this we obtain that $P \wr H$ has finite palindromic width if $P$ is a perfect group and further that $G \wr F$ has finite palindromic width for any finite, nonabelian group $F$.
 Publication:

arXiv eprints
 Pub Date:
 February 2014
 arXiv:
 arXiv:1402.4345
 Bibcode:
 2014arXiv1402.4345F
 Keywords:

 Mathematics  Group Theory
 EPrint:
 10 pages, 1 figure