# Sh:903

• Machura, M., Shelah, S., & Tsaban, B. (2010). Squares of Menger-bounded groups. Trans. Amer. Math. Soc., 362(4), 1751–1764.
• Abstract:
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 \mathbb{Z}^{\mathbb{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.
• Version 2007-02-08_11 (10p) published version (14p)
Bib entry
@article{Sh:903,
author = {Machura, Micha{\l} and Shelah, Saharon and Tsaban, Boaz},
title = {{Squares of Menger-bounded groups}},
journal = {Trans. Amer. Math. Soc.},
fjournal = {Transactions of the American Mathematical Society},
volume = {362},
number = {4},
year = {2010},
pages = {1751--1764},
issn = {0002-9947},
mrnumber = {2574876},
mrclass = {54H11 (03E17 54C65)},
doi = {10.1090/S0002-9947-09-05169-1},
note = {\href{https://arxiv.org/abs/math/0611353}{arXiv: math/0611353}},
arxiv_number = {math/0611353}
}