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 [10] 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.

中文翻译：

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最多强制对非扭转阿贝尔群进行分类 ${\mathrm{2个}}^{\mathfrak{C}}$ 具有非平凡的收敛序列

我们最多对所有基数的Abelian组进行分类 ${\mathrm{2个}}^{\mathfrak{C}}$允许一个具有非平凡收敛序列的无数紧致组。特别是，我们（一致地）回答Dikranjan和Shakhmatov [10]的问题24最多为基数${\mathrm{2个}}^{\mathfrak{C}}$，表明如果一个非扭曲的阿贝尔群最多为 ${\mathrm{2个}}^{\mathfrak{C}}$ 承认一个相当紧凑的Hausdorff群拓扑，然后它承认一个具有非平凡收敛序列的紧凑的Hausdorff群拓扑。