Occurrence problem for free solvable groups
The author studies the problem of the existence of an algorithm verifying whether systems of linear equations over a group ring of a free metabelian group are solvable. He proves that if \(G\) is a free metabelian group (of large enough rank), then the occurrence problem for right ideals of the ring \(ZG\) is undecidable. Also he shows that the occurrence problem for free solvable groups of derived length \(\geq 3\) is undecidable. It is given an example of a group with undecidable word problem which is finitely presented in the variety of solvable groups of derived length \(\geq 3\) and whose defining relations are taken from the last commutant.
scientific article; zbMATH DE number 848951