Let $n \ge 5$ . How many distinct topologies (not necessarily Hausdorff) can be given to the group $A_n$ so that it becomes a topological group ?
2026-04-02 07:02:37.1775113357
To make the alternating group a topological group
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In a possibly non-Hausdorff topological group, the closure of the identity is a normal subgroup. In a finite simple group this is either the whole group, so the topology is indiscrete, or the identity subgroup, so the topology is Hausdorff, which for a finite set must be discrete.