Palindromic width of wreath products, metabelian groups, and max-n solvable groups

Abstract A group has finite palindromic width if there exists n such that every element can be expressed as a product of n or fewer palindromic words. We show that if G has finite palindromic width with respect to some generating set, then so does G≀ℤ r $G \wr \mathbb {Z}^{r}$ . We also give a new, self-contained proof that finitely generated metabelian groups have finite palindromic width. Finally, we show that solvable groups satisfying the maximal condition on normal subgroups (max-n) have finite palindromic width.