8:53 AM
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Let $S_\omega$ denote the group of permutations of the set $\omega$ of non-negative integers. The "wobbly group" $W$ is a normal subgroup of $S_\omega$ defined by $$W = \{f\in S_\omega: \sup\{|f(n)-n|:n\in \omega\} < \infty\}.$$ Is $S_\omega/W$ isomorphic to some subgroup of $S_\omega$?

Possibly (permutations) or (permutation-groups) might be a reasonable tags for this question. (It seems that both permutation-groups and permutations have been used for permutations of infinite sets in the past.) — Martin Sleziak 59 secs ago

2 hours later…
10:40 AM
@MartinSleziak The question was deleted. The newer question on the topic already has those tags: Proper normal subgroups of $S_\omega$ containing the wobbling group.
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Let $S_\omega$ denote the group of permutations of the set $\omega$ of non-negative integers. The "wobbling subgroup" $W$ is defined by $$W = \{f\in S_\omega: \sup\{|f(n)-n|:n\in \omega\} < \infty\}.$$ Is $S_\omega$ the only normal subgroup of $S_\omega$ containing $W$?