Tilings and Submonoids of Metabelian Groups

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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 $\mathbb Z\wr (\mathbb Z\times \mathbb Z)$. 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.

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Group Theory

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http://salesiana.dossiersoluciones.com/handle/123456789/222236

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0903.0648
 http://arxiv.org/abs/0903.0648

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arXiv