Solving equations in free nilpotent groups

Abstract: "In this paper we show that any system of equations over a free nilpotent group of class c is either unitary or nullary. In fact, such a system either has a most general solution (akin to the most general solution of a system of linear diophantine equations), or every solution has a proper generalization. In principle we provide an algorithm for determining whether or not a most general solution exists, and exhibiting it if it does. This requires solving a system of linear diophantine equations for approximately c(k over c) different right hand sides, where k is the number of parameters which occur in a most general solution of the system in the variety of abelian groups."