Equations over solvable groups
Group Theory
2023-10-24 v3
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).
Keywords
Cite
@article{arxiv.2303.13240,
title = {Equations over solvable groups},
author = {Anton A. Klyachko and Mikhail A. Mikheenko and Vitaly A. Roman'kov},
journal= {arXiv preprint arXiv:2303.13240},
year = {2023}
}
Comments
7 pages. A Russian version of this paper is at http://halgebra.math.msu.su/staff/klyachko/papers.htm . V3: misprints corrected