  Using the Continuum Hyporthesis, we prove that there is a Menger-bounded
(also called o-bounded) subgroup of the Baer-Specker group Z^N, whose square is
not Menger-bounded. This settles a major open problem concerning boundedness
notions for groups, and implies that Menger-bounded groups need not be
Scheepers-bounded. This also answers some questions of Banakh, Nickolas, and
Sanchis.

General Topology;Logic