# Largest possible order of a nilpotent permutation group?

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?

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From springerlink.com/content/d6n24hgu6x180r64 , it follows that any nilpotent subgroup of $S_n$ has order less than $\sqrt{2n!}$. I can't access the article, but from the introduction, it seems this bound may be greatly improved within the paper; it talks about maximal nilpotent subgroups of $A_n$ corresponding to Sylow subgroups. –  Steve D Feb 18 '10 at 14:24