%0 Journal Article
%T Palindromic Width of Finitely Generated Solvable Groups
%A Valeriy G. Bardakov
%A Krishnendu Gongopadhyay
%J Mathematics
%D 2014
%I arXiv
%X We investigate the palindromic width of finitely generated solvable groups. We prove that every finitely generated $3$-step solvable group has finite palindromic width. More generally, we show the finiteness of palindromic width for finitely generated abelian-by-nilpotent-by-nilpotent groups. For arbitrary solvable groups of step $\geq 3$, we prove that if $G$ is a finitely generated solvable group that is an extension of an abelian group by a group satisfying the maximal condition for normal subgroups, then the palindromic width of $G$ is finite. We also prove that the palindromic width of $\mathbb Z \wr \mathbb Z$ with respect to the set of standard generators is $3$.
%U http://arxiv.org/abs/1402.6115v1