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Claudio Gorodski
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No.

If a group $G$ of rigid motions operates transitively on $\mathbb R^n$, then also the orbit of the origin is $\mathbb R^n$. But the elements of $O(n)$ all fix $0$, so $G$ must contain all translations.

Claudio Gorodski
  • 4.7k
  • 1
  • 28
  • 44