Some remarks on (a)-characterized subgroups of the circle

In recent years, Barbieri, Dikranjan, Giordano Bruno and Weber have made progress on the problem of determining which characterized subgroups of the circle group are (a-)factorizable , that is, can be written as the sum of two proper ( a -)characterized subgroups. We correct an imprecision in one of their results, [2, Theorem 5.9] from 2017, determining the countable a -characterized subgroups of T which are also a -factorizable. We also provide a revised proof of [11, Proposition 1.3] (Dikranjan, Kunen, 2007), asserting that Q / Z is characterized.