Oleg V Bryukhanov
Articles written in Proceedings – Mathematical Sciences
Volume 127 Issue 1 February 2017 pp 99-108 Research Article
We prove that the nilpotent product of a set of groups $A_1, \ldots , A_s$ has finite palindromic width if and only if the palindromic widths of $A_i$, $i = 1, \ldots , s$, 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 $n\geq 2$ and $K$ is a finite group. This result, combining with a result of Fink  gives examples of groups with infinite commutator width but finite palindromic width with respect to some generating set.