Countably compact groups without non-trivial convergent sequences

Abstract

We construct, in ZFC, a countably compact subgroup of 2c2^\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 G0\mathbb G_0 and G1\mathbb G_1 such that the product G0×G1\mathbb G_0 \times \mathbb G_1 is not countably compact, thus answering a classical problem of Comfort.