Let $G$ be a compact Hausdorff topological group. Does $G$ have torsion elements? I couldn't find examples of torsion-free compact Hausdorff topological groups. If $G$ is a Lie Group it should be true. Hausdorff cannot be omitted, because every group with the trivial topology is compact.
2026-03-26 10:59:42.1774522782
Does there exist a torsion-free compact Hausdorff topological group?
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