Geodesic
On the number of group topologies on countable groups
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2014), pp. 101-112

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If a countable group $G$ admits a non-discrete Hausdorff group topology, then the lattice of all group topologies of the group $G$ admits: – continuum $c$ of non-discrete metrizable group topologies such that $\sup\{\tau_1,\tau_2\}$ is the discrete topology for any two of these topologies; – two to the power of continuum of coatoms in the lattice of all group topologies. 
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V. I. Arnautov; G. N. Ermakova. On the number of group topologies on countable groups. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2014), pp. 101-112. http://geodesic.mathdoc.fr/item/BASM_2014_1_a6/