Algebra and Logic

, Volume 34, Issue 2, pp 112–124

Occurrence problem for free solvable groups

  • Authors
  • U. U. Umirbaev

DOI: 10.1007/BF00750164

Cite this article as:
Umirbaev, U.U. Algebr Logic (1995) 34: 112. doi:10.1007/BF00750164


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.

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© Plenum Publishing Corporation 1995