Abstract

We show that every effectively closed action of a finitely generated group G on a closed subset of {0,1}(N) can be obtained as a topological factor of the G-subaction of a (G x H-1 x H-2 )-subshift of finite type (SFT) for any choice of infinite and finitely generated groups H-1, H-2. As a consequence, we obtain that every group of the form G(1) x G(2) x G(3) admits a non-empty strongly aperiodic SFT subject to the condition that each G(i )is finitely generated and has decidable word problem. As a corollary of this last result we prove the existence of non-empty strongly aperiodic SFT in a large class of branch groups, notably including the Grigorchuk group.