Knapsack problem for nilpotent groups
А. А. Мищенко, Alexander V. Treier · journal of Groups complexity cryptology · 2017
Abstract In this work we investigate the group version of the well known knapsack problem in the class of nilpotent groups. The main result of this paper is that the knapsack problem is undecidable for any torsion-free group of nilpotency class 2 if the rank of the derived subgroup is at least 316. Also, we extend our result to certain classes of polycyclic groups, linear groups, and nilpotent groups of nilpotency class greater than or equal to 2.