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Mar 10, 2012 at 22:10 comment added Geoff Robinson Yes, but I was wondering whether the two orbits condition might force primitivity, though I couldn't imeeditaely see why
Mar 10, 2012 at 21:37 comment added Sean Eberhard I did think along these lines initially. See this question: mathoverflow.net/questions/89304/…. I don't actually care about "for all sufficiently large n" statements, so I'm happy to take n even, say, in which case you have a large transitive subgroups such as $S_\frac{n}{2} \wr C_2$.
Mar 10, 2012 at 21:27 history answered Geoff Robinson CC BY-SA 3.0