We classify the hulls of different limit-periodic potentials and show that
the hull of a limit-periodic potential is a procyclic group. We describe how
limit-periodic potentials can be generated from a procyclic group and answer
arising questions. As an expository paper, we discuss the connection between
limit-periodic potentials and profinite groups as completely as possible and
review some recent results on Schroedinger operators obtained in this context
