# Sh:903

- Machura, M., Shelah, S., & Tsaban, B. (2010).
*Squares of Menger-bounded groups*. Trans. Amer. Math. Soc.,**362**(4), 1751–1764. arXiv: math/0611353 DOI: 10.1090/S0002-9947-09-05169-1 MR: 2574876 -
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. - 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}, doi = {10.1090/S0002-9947-09-05169-1}, mrclass = {54H11 (03E17 54C65)}, mrnumber = {2574876}, mrreviewer = {Klaas Pieter Hart}, doi = {10.1090/S0002-9947-09-05169-1}, note = {\href{https://arxiv.org/abs/math/0611353}{arXiv: math/0611353}}, arxiv_number = {math/0611353} }