  We prove that if $\pi$ is a recursive set of primes, then pointlike sets are
decidable for the pseudovariety of semigroups whose subgroups are $\pi$-groups.
In particular, when $\pi$ is the empty set, we obtain Henckell's decidability
of aperiodic pointlikes. Our proof, restricted to the case of aperiodic
semigroups, is simpler than the original proof.
