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Sib. J. Pure and Appl. Math., 2018, Volume 18, Issue 4, Pages 43–55 (Mi vngu484)  

Knapsack problem for Baumslag–Solitar groups

F. A. Dudkinab, A. V. Treyerc

a Novosibirsk State University
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
c Omsk State Technical University

Abstract: In this work we investigate a decidability problem of group version of the knapsack problem for the Baumslag–Solitar group $BS(p,q)$. We proved, that the knapsack problem is decidable for the group $BS(p,q)$ for coprime integers $p > 1$, $q > 1$. In the case where $p=1$, $q\in \mathbb{N}$, we proved that the knapsack problem is decidable for the group $BS(1,q)$ with some restriction on the input of the problem. However, the problem of the decidability of the knapsack problem for the group $BS(1,q)$ on the whole set of inputs remains open.

Keywords: Baumslag–Solitar group, knapsack problem, decidability.

DOI: https://doi.org/10.33048/pam.2018.18.404

Full text: PDF file (145 kB)
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UDC: 512.543
Received: 06.03.2018

Citation: F. A. Dudkin, A. V. Treyer, “Knapsack problem for Baumslag–Solitar groups”, Sib. J. Pure and Appl. Math., 18:4 (2018), 43–55

Citation in format AMSBIB
\Bibitem{DudTre18}
\by F.~A.~Dudkin, A.~V.~Treyer
\paper Knapsack problem for Baumslag--Solitar groups
\jour Sib. J. Pure and Appl. Math.
\yr 2018
\vol 18
\issue 4
\pages 43--55
\mathnet{http://mi.mathnet.ru/vngu484}
\crossref{https://doi.org/10.33048/pam.2018.18.404}


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