### Squares of Menger-Bounded Groups

by Machura and Shelah and Tsaban. [MShT:903]

Transactions American Math Soc, 2010

Using a portion of the Continuum Hypothesis, 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.

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