Equations over solvable groups

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 t o r s i o n-f r e e 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).