Geodesic
On the number of metrizable group topologies on countable groups
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2013), pp. 17-26 
V. I. Arnautov; G. N. Ermakova. On the number of metrizable group topologies on countable groups. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2013), pp. 17-26. http://geodesic.mathdoc.fr/item/BASM_2013_2_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

If a countable group $G$ admits a non-discrete metrizable group topology $\tau_0$, then in the group $G$, there are: – Continuum of non-discrete metrizable group topologies stronger than $\tau_0$, and any two of these topologies are incomparable; – Continuum of non-discrete metrizable group topologies stronger than $\tau_0$, and any two of these topologies are comparable.

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[2] Kertesz A., Szele T.,, “On existence of non-discrete topologies on an infinite Abelian groups”, Publ. Math., 3 (1953), 187–189 | MR

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