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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.<\/jats:p>","DOI":"10.1515\/gcc-2017-0006","type":"journal-article","created":{"date-parts":[[2017,4,19]],"date-time":"2017-04-19T10:01:12Z","timestamp":1492596072000},"source":"Crossref","is-referenced-by-count":13,"title":["Knapsack problem for nilpotent groups"],"prefix":"10.1515","volume":"9","author":[{"given":"Alexei","family":"Mishchenko","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexander","family":"Treier","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","reference":[{"key":"ref91","first-page":"987","article-title":"Knapsack problems in groups","volume":"84","year":"2015","journal-title":"Math. 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