Embedding of $SO(3)$ into $S_{\infty}$

group-theory

This is a nice question which I don't have any clue.

Let $S_{\infty}$ be the group of all permutations of $\mathbb{N}.$

Is it possible to embed $SO(3)$ into $S_{\infty}?$


The answer is yes, as proved in this paper:

http://matwbn.icm.edu.pl/ksiazki/fm/fm164/fm16412.pdf

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