# Translation-like Actions and Aperiodic Subshifts on Groups

* Auteur correspondant
1 CARTE - Theoretical adverse computations, and safety
Inria Nancy - Grand Est, LORIA - FM - Department of Formal Methods
Abstract : It is well known that if $G$ admits a f.g. subgroup $H$ with a weakly aperiodic SFT (resp. an undecidable domino problem), then $G$ itself 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 $G_1 \times G_2$ 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.
Type de document :
Pré-publication, Document de travail
2015
Domaine :

https://hal.inria.fr/hal-01187069
Contributeur : Emmanuel Jeandel <>
Soumis le : mercredi 26 août 2015 - 09:05:55
Dernière modification le : jeudi 11 janvier 2018 - 06:21:25
Document(s) archivé(s) le : vendredi 27 novembre 2015 - 10:56:59

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wgroups2.pdf
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### Identifiants

• HAL Id : hal-01187069, version 1
• ARXIV : 1508.06419

### Citation

Emmanuel Jeandel. Translation-like Actions and Aperiodic Subshifts on Groups. 2015. 〈hal-01187069〉

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