Strong characterizing sequences of countable groups Original Research Article

András Biró and Vera Sós prove that for any subgroup G of image generated freely by finitely many generators there is a sequence image such that for all image we have (double vertical bar.double vertical bar denotes the distance to the nearest integer)image We extend this result to arbitrary countable subgroups of image. We also show that not only the sum of norms but the sum of arbitrary small powers of these norms can be kept small. Our proof combines ideas from the above article with new methods, involving a filter characterization of subgroups of image.