Countably compact groups without non-trivial convergent sequences

Abstract

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.

21 pages, to be published in Transactions of the American Mathematical Society