On countably compact group topologies without non-trivial convergent sequences on [formula omitted] for arbitrarily large κ and a selective ultrafilter

Abstract

Castro Pereira and Tomita showed that it is consistent that there exist arbitrarily large countably compact groups without non-trivial convergent sequences of finite order. In this paper, we obtain large p-compact groups without non-trivial convergent on the direct sum of κ copies of Q where κ=κω is infinite. In particular this gives the first arbitrarily large countably compact groups without non-trivial convergent sequences that are torsion-free.