# Countably compact groups without non-trivial convergent sequences

@article{Hruvsak2020CountablyCG, title={Countably compact groups without non-trivial convergent sequences}, author={Michael Hruvs'ak and Jan van Mill and Ulises Ariet Ramos-Garc'ia and Saharon Shelah}, journal={Transactions of the American Mathematical Society}, year={2020}, pages={1} }

We construct, in $\mathsf{ZFC}$, a countably compact subgroup of $2^{\mathfrak{c}}$ without non-trivial convergent sequences, answering an old problem of van Douwen. As a consequence we also prove the existence of two countably compact groups $\mathbb{G}_{0}$ and $\mathbb{G}_{1}$ such that the product $\mathbb{G}_{0} \times \mathbb{G}_{1}$ is not countably compact, thus answering a classical problem of Comfort.

#### 9 Citations

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Algebraic structure of countably compact non-torsion Abelian groups of size continuum from selective ultrafilters

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Assuming the existence of $\mathfrak c$ incomparable selective ultrafilters, we classify the non-torsion Abelian groups of cardinality $\mathfrak c$ that admit a countably compact group topology. We… Expand

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