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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