Tilings and Submonoids of Metabelian Groups

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Tilings and Submonoids of Metabelian Groups
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.
Markus Lohrey, Benjamin Steinberg
Added 14 May 2011
Updated 14 May 2011
Type Journal
Year 2011
Where MST
Authors Markus Lohrey, Benjamin Steinberg
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