Geodesic
Knapsack problem for Baumslag--Solitar groups
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 18 (2018) no. 4, pp. 43-55

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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. 
@article{VNGU_2018_18_4_a3,
     author = {F. A. Dudkin and A. V. Treyer},
     title = {Knapsack problem for {Baumslag--Solitar} groups},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {43--55},
     publisher = {mathdoc},
     volume = {18},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2018_18_4_a3/}
}
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F. A. Dudkin; A. V. Treyer. Knapsack problem for Baumslag--Solitar groups. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 18 (2018) no. 4, pp. 43-55. http://geodesic.mathdoc.fr/item/VNGU_2018_18_4_a3/