TY - JOUR
T1 - The diophantine problem in some metabelian groups
AU - Kharlampovich, Olga
AU - López, Laura
AU - Myasnikov, Alexei
N1 - Publisher Copyright:
© 2020 American Mathematical Society.
PY - 2020
Y1 - 2020
N2 - In this paper we show that the Diophantine problem in solvable Baumslag-Solitar groups BS(1, k) and in wreath products A | Z, where A is a finitely generated abelian group and Z is an infinite cyclic group, is decidable, i.e., there is an algorithm that, given a finite system of equations with constants in such a group, decides whether or not the system has a solution in the group.
AB - In this paper we show that the Diophantine problem in solvable Baumslag-Solitar groups BS(1, k) and in wreath products A | Z, where A is a finitely generated abelian group and Z is an infinite cyclic group, is decidable, i.e., there is an algorithm that, given a finite system of equations with constants in such a group, decides whether or not the system has a solution in the group.
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U2 - 10.1090/mcom/3533
DO - 10.1090/mcom/3533
M3 - Article
AN - SCOPUS:85106827362
SN - 0025-5718
VL - 89
SP - 2507
EP - 2519
JO - Mathematics of Computation
JF - Mathematics of Computation
IS - 325
ER -