Group is Hausdorff iff Discrete Subgroups are Closed

Theorem
A topological group is Hausdorff its discrete subgroups are closed.

Proof
Follows directly from:
 * Discrete Subgroup of Hausdorff Group is Closed
 * Topological Group is Hausdorff iff Identity is Closed

Also see

 * Group is Hausdorff iff has Closed Discrete Subgroup