2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/131772We prove that if $π$ is a recursive set of primes, then pointlike sets are decidable for the pseudovariety of semigroups whose subgroups are $π$-groups. In particular, when $π$ 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.Group Theory20M07text