We say that a finitely generated group Γ is self-simulable if every effectively closed action of Γ on a closed subset of 0, 1 N \ {0, 1\}^ {N} is the topological factor of a Γ -subshift of finite type. We show that self-simulable groups exist, that any direct product of non-amenable finitely generated groups is self-simulable, that under technical conditions self-simulability is inherited from subgroups, and that the subclass of self-simulable groups is stable under commensurability and quasi-isometries of finitely presented groups. Some notable examples of self-simulable groups obtained are the direct product F k × F k Fₖ Fₖ of two free groups of rank k ≥ 2 k 2, non-amenable finitely generated branch groups, the simple groups of Burger and Mozes, Thompson’s V V, the groups GL n (Z) GLₙ (Z), SL n (Z) SLₙ (Z), A u t (F n) Aut (Fₙ) and <inline-formula content-type="math/ma
Barbieri et al. (2026) studied this question.