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Ali Taghavi
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Free action of symmetric groups

What type of compact manifolds, can be acted freely by symmetric group $S_{m}$ for some $m>2$?

Is there a compact manifold which can be act freely by all symmetric groups $S_{m}$?

This question have been asked already here and is indirectly related to this.

Ali Taghavi
  • 356
  • 8
  • 31
  • 123