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Questions about the branch of algebra that deals with groups.

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Is $\text{Sym}(\omega)/\text{(fin)}$ embeddable in $\text{Sym}(\omega)$?

$Sym(\omega)$ has what is called the "automatic continuity property", whence any morphism from $Sym(\omega)$ to a Polish group $G$ which is trivial on $(fin)$ is the identity (by density of $(fin)$ an …
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