%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