Equations over solvable groups

Not any nonsingular equation over a metabelian group has solution in a larger metabelian group. However, any nonsingular equation over a solvable group with a subnormal series with abelian torsion-free quotients has a solution in a larger group with a similar subnormal series of the same length (and...

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Bibliographic Details
Published in:Journal of algebra 2024-01, Vol.638, p.739-750
Main Authors: Klyachko, Anton A., Mikheenko, Mikhail A., Roman'kov, Vitaly A.
Format: Article
Language:English
Subjects:
Equations over groups
Group extensions
Group rings
Group theory
Howie conjecture
Metabelian groups
Quasivarieties of groups
Solvable groups
Systems of equations over groups
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Summary:Not any nonsingular equation over a metabelian group has solution in a larger metabelian group. However, any nonsingular equation over a solvable group with a subnormal series with abelian torsion-free quotients has a solution in a larger group with a similar subnormal series of the same length (and an analogous fact is valid for systems of equations).
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2023.10.004