Forcing a classification of non-torsion Abelian groups of size at most $2^{\mathfrak{c}}$ with non-trivial convergent sequences

Abstract

We force a classification of all the Abelian groups of cardinality at most $2^{\mathfrak{c}}$ that admit a countably compact group with a non-trivial convergent sequence. In particular, we answer (consistently) Question 24 of Dikranjan and Shakhmatov for cardinality at most $2^{\mathfrak{c}}$, by showing that if a non-torsion Abelian group of size at most $2^{\mathfrak{c}}$ admits a countably compact Hausdorff group topology, then it admits a countably compact Hausdorff group topology with non-trivial convergent sequences.

arXiv admin note: text overlap with arXiv:1909.03340