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Knapsack problem for nilpotent groups

Group Theory 2016-06-29 v1

Abstract

We prove that Knapsack problem (KP) is undecidable for any group of nilpotency class two if the number of generators (without torsion) of the derived subgroup is at least 322. This result together with the fact that if KP is undecidable for a subgroup then it undecidable for the whole group allows us extend our result to certain classes of polycyclic groups, linear groups and nilpotent groups of higher nilpotency class.

Keywords

Cite

@article{arxiv.1606.08584,
  title  = {Knapsack problem for nilpotent groups},
  author = {Alexei Mishchenko and Alexander Treier},
  journal= {arXiv preprint arXiv:1606.08584},
  year   = {2016}
}

Comments

14 pages

R2 v1 2026-06-22T14:36:17.301Z