Knapsack problem for nilpotent groups
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Alexei Mishchenko
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.
Funding source: Russian Science Foundation
Award Identifier / Grant number: 14-11-00085
Funding statement: The research was supported by the Russian Science Foundation, project no. 14-11-00085.
Acknowledgements
The authors are grateful to A. Miasnikov and A. Nikolaev for discussions and to the referee for attention to this work and advice.
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Articles in the same Issue
- Frontmatter
- Pseudo-free families of finite computational elementary abelian p-groups
- Cryptography from the tropical Hessian pencil
- Public-key cryptosystem based on invariants of diagonalizable groups
- The isomorphism problem for torsion free nilpotent groups of Hirsch length at most 5
- Log-space conjugacy problem in the Grigorchuk group
- Knapsack problem for nilpotent groups
Articles in the same Issue
- Frontmatter
- Pseudo-free families of finite computational elementary abelian p-groups
- Cryptography from the tropical Hessian pencil
- Public-key cryptosystem based on invariants of diagonalizable groups
- The isomorphism problem for torsion free nilpotent groups of Hirsch length at most 5
- Log-space conjugacy problem in the Grigorchuk group
- Knapsack problem for nilpotent groups
