Short, highly imprimitive words yield hyperbolic one-relator groups

TL;DR

This paper provides experimental evidence supporting the conjecture that words with imprimitivity rank greater than two produce hyperbolic one-relator groups, contributing to understanding the structure of such groups.

Contribution

It offers experimental validation for a conjecture linking imprimitivity rank of words to hyperbolicity in one-relator groups.

Findings

Words of imprimitivity rank > 2 tend to generate hyperbolic groups

Experimental data supports Louder and Wilton's conjecture

Enhances understanding of the relationship between word properties and group hyperbolicity

Abstract

We give experimental support for a conjecture of Louder and Wilton saying that words of imprimitivity rank greater than two yield hyperbolic one-relator groups.