Stability of Nilpotent Groups of Class 2 and Prime Exponent

Let p be an odd prime. A method is described which given a structure M of finite similarity type produces a nilpotent group of class 2 and exponent p which is in the same stability class as M. THEOREM. There are nilpotent groups of class 2 and exponent p in all stability classes. THEOREM. The problem of characterizing a stability class is equivalent to characterizing the (nilpotent, class 2, exponent p) groups in that class. A goal in applied model theory has been to characterize the various stability classes of algebraic systems. Although there has been some success (eg. abelian groups), for most algebraic systems only partial results have been obtained. In (2) it is suggested that the problem of characterizing the wo-stable groups is intractable. Here we will explain why. A construction is described which given a structure (of