The fully residually F quotients of F*<x,y>

TL;DR

This paper characterizes fully residually free quotients, known as limit groups, derived from systems of equations with two variables over a free group, expanding understanding of their algebraic structure.

Contribution

It provides a detailed description of fully residually free quotients arising from two-variable systems over a free group, enriching the theory of limit groups.

Findings

Identification of all fully residually F quotients from two-variable systems

Connection between systems of equations and limit groups

Advancement in understanding the structure of free group quotients

Abstract

We describe the fully residually F; or limit groups relative to F; (where F is a free group) that arise from systems of equations in two variables over F that have coefficients in F.