I'm trying to obtain a bound for the order of some finite groups, and part of it comes down to the order of a permutation group of degree $n$ that is nilpotent. I imagine these have to be much smaller than the full symmetric group, and a bound that is sub-exponential in $n$ would seem reasonable (given that permutation $p$-groups fall a long way short of having exponential order), but I haven't seen this written down anywhere.

I found one reference that looks promising:

P. Palfy, Estimations for the order of various permutation groups, Contributions to general algebra, 12 (Vienna, 1999), 37-49, Heyn, Klagenfurt, 2000.

However, I can't actually find the article anywhere online. Any suggestions?