Palindromic widths of graph of groups

TL;DR

This paper investigates the palindromic width of complex group constructions, proving it is generally infinite for HNN extensions, amalgamated free products, and fundamental groups of graphs of groups.

Contribution

It establishes the infinitude of palindromic width for various group constructions, extending understanding of their algebraic properties.

Findings

Palindromic width of HNN extensions is infinite.

Palindromic width of amalgamated free products is infinite, except in specific cases.

Fundamental groups of graphs of groups mostly have infinite palindromic width.

Abstract

We prove that the palindromic width of HNN extension of a group by proper associated subgroups is infinite. We also prove that the palindromic width of the amalgamated free product of two groups via a proper subgroup is infinite (except when the amalgamated subgroup has index two in each of the factors). Combining these results it follows that the palindromic width of the fundamental group of a graph of groups is mostly infinite.