| Abstract: | We study the problem on the existence of an algorithm verifying whether systems of linear equations over a group ring of a free metabelian group are solvable. The occurrence problem for free solvable groups of derived length  3is proved undecidable. We give an example of a group with undecidable word problem which is finitely presented in a variety of solvable groups and is defined by the relations from the last commutator subgroup.
Translated fromAlgebra i Logika, Vol. 34, No. 2, pp. 211-232, March-April, 1995. |
