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Jan 10, 2013 at 13:15 comment added Nick Gill Derek, of course you are right, as your citation of the Praeger-Saxl result makes clear.
Jan 10, 2013 at 11:48 comment added Derek Holt But the conclusion will be that, at least for large enough $n$, primitive groups will not be the largest groups with the required property.
Jan 10, 2013 at 10:15 history answered Nick Gill CC BY-SA 3.0