Topologies on groups determined by discrete subsets

Let G be an infinite group. Given a filter F on G, let TF] denote the largest left invariant topology on G in which F converges to the identity. In this paper, we study the topology TF] in case when F contains the Fréchet filter and there is such that all the subsets xM(x), where x∈G, are pairwise disjoint. We show that TF] possesses interesting extremal properties. We consider also the question whether TF] can be a group topology.