  In this note we prove the following results:
  $\bullet$ 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.
  $\bullet$ 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 $\mathbb{Z}\times
G$. In particular, this is true for the free group with 2 generators,
Thompson's groups $T$ and $V$, $PSL_2(\mathbb{Z})$ and any f.g. group of
rational matrices which is bounded.
