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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
Entstehung:
Anmerkungen:
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].