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.

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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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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/

[1] Markov A. A., “On absolutely closed sets”, Mat. Sb., 18(60):1 (1945), 3–28 (in Russian) | MR | Zbl

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

[3] Ol'shansky A. Yu., “Remark on countable non-topologizable group”, Vestnik MGU. Ser. Mat. i Mech., 1980, no. 3, 103 (in Russian)

[4] Bourbaki N., Topologie generale, Moskva, 1958 (in Russian)

[5] Engelking R., General topology, Moskva, 1986 (in Russian) | MR