Palindromic Width of Finitely Generated Solvable Groups

Abstract

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 $\ge 3$, 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 $3$.

References in corpus (3)

• Palindromic primitives and palindromic bases in the free group of rank two
• Palindromic width of wreath products, metabelian groups, and max-n solvable groups
• On palindromic width of certain extensions and quotients of free nilpotent groups