Theory of Computing Systems

, Volume 48, Issue 2, pp 411–427 | Cite as

Tilings and Submonoids of Metabelian Groups



In this paper we show that membership in finitely generated submonoids is undecidable for the free metabelian group of rank 2 and for the wreath product ℤ(ℤ×ℤ). We also show that subsemimodule membership is undecidable for finite rank free (ℤ×ℤ)-modules. The proof involves an encoding of Turing machines via tilings. We also show that rational subset membership is undecidable for two-dimensional lamplighter groups.


Metabelian groups Lamplighter groups Submonoids Rational subsets Decision problems in group theory 


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Institut für InformatikUniversität LeipzigLeipzigGermany
  2. 2.School of Mathematics and StatisticsCarleton UniversityOttawaCanada

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