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.

• Type: Journal
• Year: 2011
• Where: MST
• Authors: Markus Lohrey, Benjamin Steinberg
• Keywords: Free Metabelian Group, Hardware, MST 2011, Rational Subset Membership, Two-dimensional Lamplighter Groups