Tilings and Submonoids of Metabelian Groups

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dc.creatorLohrey, Markus
dc.creatorSteinberg, Benjamin
dc.date2009-03-03
dc.date.accessioned2026-07-07T12:48:57Z
dc.date.available2026-07-07T12:48:57Z
dc.descriptionIn 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 $\mathbb Z\wr (\mathbb Z\times \mathbb Z)$. We also show that subsemimodule membership is undecidable for finite rank free $(\mathbb Z\times \mathbb Z)$-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.
dc.identifierhttps://arxiv.org/abs/0903.0648
dc.identifierhttp://arxiv.org/abs/0903.0648
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/222236
dc.subjectGroup Theory
dc.titleTilings and Submonoids of Metabelian Groups
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