Solvability of equations in classes of solvable groups and Lie algebras

DOI10.1007/s10469-017-9445-6zbMath1379.20011OpenAlexW2763019074WikidataQ115384426 ScholiaQ115384426MaRDI QIDQ683377

Vitaliĭ Roman'kov

Publication date: 6 February 2018

Published in: Algebra and Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10469-017-9445-6

Mathematics Subject Classification ID

Solvable groups, supersolvable groups (20F16) Associated Lie structures for groups (20F40) Algebraic geometry over groups; equations over groups (20F70)

Cites Work

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• Diophantine questions in the class of finitely generated nilpotent groups
• The commutator width of some relatively free Lie algebras and nilpotent groups
• Equational Noetherianness of rigid soluble groups.
• Irreducible algebraic sets over divisible decomposed rigid groups.
• Coproducts of rigid groups.
• Krull dimension of solvable groups.
• Unsolvability of the endomorphic reducibility problem in free nilpotent groups and in free rings
• On rationality of verbal subsets in a group
• Algebraically and verbally closed subgroups and retracts of finitely generated nilpotent groups
• Equations over groups

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