Hurwitz equivalences of positive group generators

TL;DR

This paper introduces a criterion and an algorithmic approach for determining Hurwitz equivalences among positive group generators, enhancing understanding of their structural relationships in positively presented groups.

Contribution

It provides a new criterion and an algorithm based on word reversing to decide Hurwitz equivalence and conjugation among positive generators in groups.

Findings

Established a criterion for Hurwitz equivalence of positive generators.

Developed an algorithm using word reversing for the equivalence decision process.

Enhanced tools for analyzing generator relationships in positively presented groups.

Abstract

For a positively presented group G, we provide a criterion for two tuples of positive group generators of G to be Hurwitz equivalent or Hurwitz-conjugation equivalent. We also present an algorithmic approach to solve the Hurwitz equivalence and the Hurwitz search problems by using the word reversing method.