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Sep 22, 2010 at 13:23 comment added Simon Thomas @Mark: Fair enough!
Sep 22, 2010 at 13:08 history edited user6976 CC BY-SA 2.5
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Sep 22, 2010 at 13:06 comment added user6976 @Simon: OK, I was too quick. I meant all finite groups (because they are all in $S_\infty$. I have modified the answer.
Sep 22, 2010 at 12:43 comment added Simon Thomas In fact, isn't your group the finitary permutations of $\mathbb{Z}$ extended by the shift? If so, it certainly doesn't contain all countable locally finite groups ....
Sep 22, 2010 at 11:37 comment added Simon Thomas Could you say a little more about why every countable locally finite group embeds in your group? (The construction of Hall's universal locally finite group proceeds by iterating the left regular permutation representation ... how does the shift manage this?)
Sep 22, 2010 at 10:39 history answered user6976 CC BY-SA 2.5