On Palindromic Widths of Nilpotent and Wreathe Products

Abstract

We prove that the nilpotent product of a set of groups $A_1,\dots ,A_s$ has finite palindromic width if and only if the palindromic widths of $A_i,i=1,\dots ,s,$ are finite. We give a new proof that the commutator width of $F_n\wr K$ is infinite, where $F_n$ is a free group of rank $n\ge 2$ and $K$ a finite group. This result, combining with a result of Fink \cite{f1} gives examples of groups with infinite commutator width but finite palindromic width with respect to some generating set.

re-organized version; references added

References in corpus (2)

• Palindromic primitives and palindromic bases in the free group of rank two
• Conjugacy Growth and Conjugacy Width of Certain Branch Groups