ON THE SOLUTIONS OF EQUATIONS OVER NILPOTENT GROUPS OF CLASS 2

Abstract

In this paper, we study equations over nilpotent groups of class 2. We show that there are some overgroups which contains solutions of equations with exponent sum 1 over nilpotent groups of class 2. As known, equations over a field has a solution in an extension field which contains a copy of the given field. But it is not easy to find that a solution of equations over groups. In many cases, even if equations over groups has a solution, the overgroup is not concrete but very Here we find the concrete overgroups in case of nilpotent groups.