  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.
