Aperiodic Subshifts of Finite Type on Groups

Emmanuel Jeandel 1, *
* Corresponding author
1 CARTE - Theoretical adverse computations, and safety
Inria Nancy - Grand Est, LORIA - FM - Department of Formal Methods
Abstract : In this note we prove the following results: • 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. • 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 , P SL2(Z) and any f.g. group of rational matrices which is bounded.
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https://hal.inria.fr/hal-01110211
Contributor : Emmanuel Jeandel <>
Submitted on : Friday, July 3, 2015 - 11:04:28 AM
Last modification on : Tuesday, December 18, 2018 - 4:48:02 PM
Long-term archiving on : Tuesday, April 25, 2017 - 10:34:11 PM

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  • HAL Id : hal-01110211, version 2
  • ARXIV : 1501.06831

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Emmanuel Jeandel. Aperiodic Subshifts of Finite Type on Groups. 2015. ⟨hal-01110211v2⟩

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