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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-trivialconvergent sequence. In particular, we answer (consistently) Question 24 ofDikranjan and Shakhmatov for cardinality at most $2^{\mathfrak c}$, by showingthat if a non-torsion Abelian group of size at most $2^\mathfrak c$ admits acountably compact Hausdorff group topology, then it admits a countably compactHausdorff group topology with non-trivial convergent sequences.

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