2015/08/26 by Emmanuel Jeandel, Jeandel, Emmanuel
Computer Science · Mathematics · #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Formal Languages and Automata Theory (cs.FL) #Group Theory (math.GR) #Mathematical Dynamics and Fractals #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1508.06419
openalex publication_date 2015/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is well known that if G admits a f.g. subgroup H with a weaklyaperiodic SFT (resp. an undecidable domino problem), then Gitself has a weakly aperiodic SFT (resp. an undecidable domino problem).We prove that we can replace the property "H is a subgroup of G"by "H acts translation-like on G", provided H is finitely presented.In particular:* If G_1 and G_2 are f.g. infinite groups, then G_1 × G_2 has a weakly aperiodic SFT (and actually a undecidable domino problem). In particular the Grigorchuk group has an undecidable domino problem. * Every infinite f.g. p-group admits a weakly aperiodic SFT.