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Assumindo a existencia de $\\mathfrak c$ ultrafiltros seletivos dois a dois incomparaveis (segundo a ordem de Rudin-Keisler) provamos que o grupo abeliano livre de cardinalidade $\\mathfrak c$ admite uma topologia de grupo enumeravelmente compacta com uma sequencia nao trivial convergente. Sob as mesmas hipoteses, mostramos que um grupo topologico abeliano quase livre de torcao $(G, +, \\tau)$ com $|G| = |\\tau| = \\mathfrak c$ admite uma topologia independente de $\\tau$ que o torna um grupo topologico e caracterizamos algebricamente os grupos abelianos de nao torcao que tem cardinalidade $\\mathfrak c$ e que admitem uma topologia de grupo enumeravelmente compacta (sem sequencias nao triviais convergentes). Provamos, ainda, que o grupo abeliano livre de cardinalidade $\\mathfrak c$ admite uma topologia de grupo que torna seu quadrado enumeravelmente compacto e construimos um semigrupo de Wallace cujo quadrado e, tambem, enumeravelmente compacto. Por fim, assumindo a existencia de $2^{\\mathfrak c}$ ultrafiltros seletivos, garantimos que se um grupo abeliano de nao torcao e cardinalidade $\\mathfrak c$ admite uma topologia de grupo enumeravelmente compacta, entao o mesmo admite $2^{\\mathfrak c}$ topologias de grupo enumeravelmente compactas (duas a duas nao homeomorfas).%%%%Assuming the existence of $\\mathfrak c$ pairwise incomparable selective ultrafilters (according to the Rudin-Keisler ordering) we prove that the free abelian group of cardinality $\\mathfrak c$ admits a countably compact group topology that contains a non-trivial convergent sequence. Under the same hypothesis, we show that an abelian almost torsion-free topological group $(G, +, \\tau)$ with $|G| = |\\tau| = \\mathfrak c$ admits a group topology independent of $\\tau$ and we algebraically characterize the non-torsion abelian groups of cardinality $\\mathfrak c$ which admit a countably compact group topology (without non-trivial convergent sequences). We also prove that the free abelian group of cardinality $\\mathfrak c$ admits a group topology that makes its square countably compact and we construct a Wallace\'s semigroup whose square is countably compact. Finally, assuming the existence of $2^{\\mathfrak c}$ selective ultrafilters, we ensure that if a non-torsion abelian group of cardinality $\\mathfrak c$ admits a countably compact group topology, then it admits $2^{\\mathfrak c}$ (pairwise non-homeomorphic) countably compact group topologies.

Topologias enumeravelmente compactas em grupos abelianos de não torção via ultrafiltros seletivos