2015/01/27 by Emmanuel Jeandel, Jeandel, Emmanuel
Computer Science · Mathematics · #Cellular Automata and Applications #Discrete Mathematics (cs.DM) #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Group Theory (math.GR) #Mathematical Dynamics and Fractals #cs.DM #math.DS #math.GR #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1501.06831
New version. Adding results about monster groups
openalex publication_date 2015/01/27 · arxiv created 2015/07/04 · arxiv updated 2015/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note we prove the following results: \bullet If a finitely presented group G admits a strongly aperiodic SFT, then G has decidable word problem. More generally, for f.g. groups that are not recursively presented, there exists a computable obstruction for them to admit strongly aperiodic SFTs. \bullet On the positive side, we build strongly aperiodic SFTs on some new classes of groups. We show in particular that some particular monster groups admits strongly aperiodic SFTs for trivial reasons. Then, for a large class of group G, we show how to build strongly aperiodic SFTs over ℤ× G. In particular, this is true for the free group with 2 generators, Thompson's groups T and V, PSL2(ℤ) and any f.g. group of rational matrices which is bounded.