Undecidability of the submonoid membership problem for a sufficiently large finite direct power of the Heisenberg group

DOI10.33048/SEMI.2023.20.024MaRDI QIDQ6587386

Vitaliĭ Roman'kov

Publication date: 14 August 2024

Published in: Sibirskie Elektronnye Matematicheskie Izvestiya (Search for Journal in Brave)

zbMATH Keywords

nilpotent groupHeisenberg groupHilbert's 10th problemsubmonoid membership probleminterpretability of diophantine equations in groups

Mathematics Subject Classification ID

Nilpotent groups (20F18) Semigroups in automata theory, linguistics, etc. (20M35) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10)

Cites Work

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• Positive elements and sufficient conditions for solvability of the submonoid membership problem for nilpotent groups of class two
• The rational subset membership problem for groups: a survey
• Reduction of an arbitrary diophantine equation to one in 13 unknowns
• On homomorphisms onto finite groups
• On the Identity Problem for the Special Linear Group and the Heisenberg Group.
• Algorithmic theory of solvable groups
• On Reachability Problems for Low-Dimensional Matrix Semigroups
• Complexity and Randomness in Group Theory

Related Items (1)

Semigroup intersection problems in the Heisenberg groups

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