Squares of menger-bounded groups

Michal Machura; Saharon Shelah; Boaz Tsaban

doi:10.1090/S0002-9947-09-05169-1

Squares of menger-bounded groups

Michal Machura^*
, Saharon Shelah
, Boaz Tsaban

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

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 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.

Original language	English
Pages (from-to)	1751-1764
Number of pages	14
Journal	Transactions of the American Mathematical Society
Volume	362
Issue number	4
DOIs	https://doi.org/10.1090/S0002-9947-09-05169-1
State	Published - Apr 2010

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10.1090/S0002-9947-09-05169-1

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AB - 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 ℤℕ, 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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Squares of menger-bounded groups

Abstract

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