The JSJ-decompositions of one-relator groups with torsion

TL;DR

This paper uses JSJ-decompositions to formalize and partially prove a folk conjecture about the structure of one-relator groups with torsion, showing they resemble torsion-free hyperbolic groups.

Contribution

It formalizes a folk conjecture using JSJ-decompositions and proves a weaker version linking one-relator groups with torsion to hyperbolic groups.

Findings

Partial proof of the folk conjecture

One-relator groups with torsion resemble hyperbolic groups

Structure closely related to torsion-free hyperbolic groups

Abstract

In this paper we use JSJ-decompositions to formalise a folk conjecture recorded by Pride on the structure of one-relator groups with torsion. We prove a slightly weaker version of the conjecture, which implies that the structure of one-relator groups with torsion closely resemble the structure of torsion-free hyperbolic groups.