• Medientyp: E-Artikel
  • Titel: Quadratic equations in metabelian Baumslag–Solitar groups
  • Beteiligte: Mandel, Richard; Ushakov, Alexander
  • Erschienen: World Scientific Pub Co Pte Ltd, 2023
  • Erschienen in: International Journal of Algebra and Computation, 33 (2023) 6, Seite 1195-1216
  • Sprache: Englisch
  • DOI: 10.1142/s0218196723500558
  • ISSN: 0218-1967; 1793-6500
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  • Beschreibung: For a finitely generated group G, the Diophantine problem over G is the algorithmic problem of deciding whether a given equation [Formula: see text] (perhaps restricted to a fixed subclass of equations) has a solution in G. In this paper, we investigate the algorithmic complexity of the Diophantine problem for the class [Formula: see text] of quadratic equations over the metabelian Baumslag–Solitar groups [Formula: see text]. We prove that this problem is [Formula: see text]-complete whenever [Formula: see text], and determine the algorithmic complexity for various subclasses (orientable, nonorientable, etc.) of [Formula: see text].