Knapsack problem for nilpotent groups

DOI10.1515/gcc-2017-0006zbMath1382.20039arXiv1606.08584OpenAlexW2963766185MaRDI QIDQ524650

Alexei A. Mishchenko, Alexander V. Treier

Publication date: 3 May 2017

Published in: Groups, Complexity, Cryptology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.08584

zbMATH Keywords

undecidabilitynilpotent groupsknapsack problem

Mathematics Subject Classification ID

Nilpotent groups (20F18) Undecidability and degrees of sets of sentences (03D35) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10)

Related Items (8)

Decidability problem for exponential equations in finitely presented groups ⋮ Knapsack and the power word problem in solvable Baumslag–Solitar groups ⋮ On the Identity Problem for the Special Linear Group and the Heisenberg Group. ⋮ Closure properties of knapsack semilinear groups ⋮ Unnamed Item ⋮ Knapsack in hyperbolic groups ⋮ Low-complexity computations for nilpotent subgroup problems ⋮ Knapsack Problems for Wreath Products

Cites Work

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• Knapsack problems in products of groups
• The decision problem for exponential diophantine equations
• Constructing faithful representations of finitely-generated torsion-free nilpotent groups
• Equations in nilpotent groups
• Knapsack and subset sum problems in nilpotent, polycyclic, and co-context-free groups
• Universal diophantine equation
• Knapsack in graph groups, HNN-extensions and amalgamated products
• Knapsack problems in groups

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