Abstract Recently, P. Das, A. Ghosh and T. Aziz have given a criterion for statistically characterized subgroups of the circle group ℝ/ℤ to be torsion. Here we give a completely different and much shorter proof of this result. Moreover, we give for a characterized subgroup of ℝ/ℤ a sufficient condition to be torsion, unifying and generalizing earlier results.
Hans Weber (Mon,) studied this question.