# 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.
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