Let p be a (fixed)
prime number. Define f(n,p) as the number of isomorphism classes of groups of order p^n. Then: :f(n,p) = p^{\frac{2}{27}n^3 + \mathcal O(n^{8/3})} Here, the
big-O notation is with respect to n, not with respect to p (the constant under the big-O notation may depend on p). == References ==