Universal input of knapsack problem for groups

In this work we investigate the group version of the well known knapsack problem (KP) in class of nilpotent groups. We show that there exists the universal input for this problem. In other word it mean that there is the two step nilpotent group G_u and parametric input I_n, where n is natural parameter, such that for any torsion free nilpotent group G and input I for KP there exists a natural number m such that KP for group G_u on input I_m is equivalent to KP for group G on input I.