A note on unbounded strongly measure zero subgroups of the Baer–Specker group

We show that it is consistent with ZFC that there exist:(1) ounded (with respect to ⩽ ∗ ) and strongly measure zero subgroup of Z N , but without the Menger property. ounded (with respect to ⩽ ∗ ) and strongly measure zero subgroup of Z N with the Menger property which does not have the Rothberger property. answers the last two problems which remained from a classification project of Machura and Tsaban.