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arXiv · 2303.13240

Equations over solvable groups

Anton A. Klyachko·Mikhail A. Mikheenko·Vitaly A. Roman'kov
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Abstract

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).

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Anton A. Klyachko, Mikhail A. Mikheenko, Vitaly A. Roman'kov. 2023-03-23. Equations over solvable groups. https://doi.org/10.1016/j.jalgebra.2023.10.004

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