One Relator Quotients of Graph Products

TL;DR

This paper extends classical results on one-relator groups to certain graph products, providing new insights into their algebraic structure and decision problems.

Contribution

It generalizes Magnus' Freiheitssatz and the word problem solution to one relator quotients of right-angled Artin groups and graph products of locally indicable polycyclic groups.

Findings

Generalization of Freiheitssatz to new classes of groups

Solution to the word problem in these groups

Enhanced understanding of algebraic properties of graph products

Abstract

In this paper, we generalise Magnus' Freiheitssatz and solution to the word problem for one-relator groups by considering one relator quotients of certain classes of right-angled Artin groups and graph products of locally indicable polycyclic groups.