Computing equations for residually free groups

Abstract

We show that there is no algorithm deciding whether the maximal residually free quotient of a given finitely presented group is finitely presentable or not.

Given a finitely generated subgroup $G$ of a finite product of limit groups, we discuss the possibility of finding an explicit set of defining equations (i.e., of expressing $G$ as the maximal residually free quotient of an explicit finitely presented group).