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Tilings and Submonoids of Metabelian Groups

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Abstract

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.

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Authors and Affiliations

  1. Institut für Informatik, Universität Leipzig, Leipzig, Germany

    Markus Lohrey

  2. School of Mathematics and Statistics, Carleton University, Ottawa, ON, Canada

    Benjamin Steinberg

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  1. Markus Lohrey
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  2. Benjamin Steinberg
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Correspondence to Markus Lohrey.

Additional information

The authors would like to acknowledge the support of DFG Mercator program. The second author is also supported by an NSERC grant.

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Lohrey, M., Steinberg, B. Tilings and Submonoids of Metabelian Groups. Theory Comput Syst 48, 411–427 (2011). https://doi.org/10.1007/s00224-010-9264-9

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