Palindromic width of free nilpotent groups

TL;DR

This paper investigates the palindromic width of free nilpotent groups, establishing its finiteness for finitely generated cases and abelian-by-nilpotent groups, contributing to understanding their algebraic structure.

Contribution

It proves the finiteness of palindromic width in free nilpotent and abelian-by-nilpotent groups, extending previous knowledge in group theory.

Findings

Palindromic width of finitely generated free nilpotent groups is finite.

Palindromic width of free abelian-by-nilpotent groups is finite.

Provides new insights into the structure of these groups.

Abstract

In this paper we consider the palindromic width of free nilpotent groups. In particular, we prove that the palindromic width of a finitely generated free nilpotent group is finite. We also prove that the palindromic width of a free abelian-by-nilpotent group is finite.