Countably compact group topologies on non-torsion abelian groups of size continuum with non-trivial convergent sequences

{Matheus Koveroff Bellini, Ana Carolina Boero, Irene Castro Pereira, Vinicius de Oliveira Rodrigues, Artur Hideyuki Tomita

Published 2018-10-11Version 1

Under $\mathfrak{p} = \mathfrak{c}$, we answer Question 24 of \cite{dikranjan&shakhmatov3} for cardinality ${\mathfrak c}$ , by showing that if a non-torsion Abelian group of size continuum admits a countably compact Hausdorff group topology, then it admits a countably compact Hausdorff group topology with non-trivial convergent sequences.