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Knapsack problem for nilpotent groups

Knapsack problem for nilpotent groups AbstractIn 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Groups Complexity Cryptology de Gruyter

Knapsack problem for nilpotent groups

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Publisher
de Gruyter
Copyright
© 2017 by De Gruyter
ISSN
1869-6104
eISSN
1869-6104
DOI
10.1515/gcc-2017-0006
Publisher site
See Article on Publisher Site

Abstract

AbstractIn 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.

Journal

Groups Complexity Cryptologyde Gruyter

Published: May 1, 2017

References