, Volume 34, Issue 2, pp 112-124

Occurrence problem for free solvable groups

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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.