Diophantine questions in the class of finitely generated nilpotent groups

DOI10.1515/jgth-2016-0504zbMath1361.20025OpenAlexW2325273846MaRDI QIDQ285579

Vitaliĭ Roman'kov

Publication date: 19 May 2016

Published in: Journal of Group Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/jgth-2016-0504

zbMATH Keywords

nilpotent groupsDiophantine problemendomorphism problemretract problemunsolvability

Mathematics Subject Classification ID

Nilpotent groups (20F18) Decidability of theories and sets of sentences (03B25) Mechanization of proofs and logical operations (03B35) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Algebraic geometry over groups; equations over groups (20F70)

Related Items (7)

Algebraically and verbally closed subgroups and retracts of finitely generated nilpotent groups ⋮ Solvability of independent systems of equations in finitely generated nilpotent groups ⋮ Post's correspondence problem: from computer science to algebra ⋮ Post's Correspondence Problem for hyperbolic and virtually nilpotent groups ⋮ Solvability of equations in classes of solvable groups and Lie algebras ⋮ Orientable quadratic equations in free metabelian groups ⋮ Low-complexity computations for nilpotent subgroup problems

Cites Work

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• Model-theoretic and algorithmic questions in group theory
• An algorithmic problem for nilpotent groups and rings
• Unsolvability of the endomorphic reducibility problem in free nilpotent groups and in free rings
• Equations over groups
• Reduction of an arbitrary diophantine equation to one in 13 unknowns
• Equations in free metabelian groups

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