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. • For a large class of group G, Z × G admits a strongly aperiodic SFT. 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.