In the following post by DavidLHarden :
[See Here][1]


  [1]: http://mathoverflow.net/questions/68109/orders-of-automorphism-groups-of-p-groups

He quoted the following claim:
"There is a theorem that says that if $p$ is  a prime and $|G|=p^n $ , then $|AutG| $ divides 
$ \Pi_{k=0}^{n-1} (p^{n}-p^{k}) $ " . 

I can't find any reference for this theorem , and although Jr. Hall gives something similar as theorem 12.2, it still isn't in this form.

Does someone know of any reference for this fact?


Thanks in advance